Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 36}{x - 6}\), on its original real domain.

Find the excluded input of the original expression.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 49}{x - 7}\), on its original real domain.

Find the excluded input of the original expression.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 49}{x - 7}\), on its original real domain.

Write the simplified expression as x+k. Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 64}{x - 8}\), on its original real domain.

Write the simplified expression as x+k. Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 64}{x - 8}\), on its original real domain.

Evaluate F at \(\displaystyle x=13\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 4}{x - 2}\), on its original real domain.

Evaluate F at \(\displaystyle x=8\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 4}{x - 2}\), on its original real domain.

Solve \(\displaystyle F(x)=10\) on the original domain.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle F(x)=\frac{x^{2} - 9}{x - 3}\), on its original real domain.

Solve \(\displaystyle F(x)=13\) on the original domain.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{3}{x - 2}\) and \(\displaystyle B=\)\(\displaystyle \frac{8}{x - 5}\). Every operation uses the common original domain \(\displaystyle x\ne 2, 5\).

Write A+B over denominator \(\left(x - 5\right) \left(x - 2\right)\). Find the x coefficient in its numerator.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{4}{x - 3}\) and \(\displaystyle B=\)\(\displaystyle \frac{9}{x - 7}\). Every operation uses the common original domain \(\displaystyle x\ne 3, 7\).

Write A+B over denominator \(\left(x - 7\right) \left(x - 3\right)\). Find the x coefficient in its numerator.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{4}{x - 3}\) and \(\displaystyle B=\)\(\displaystyle \frac{9}{x - 7}\). Every operation uses the common original domain \(\displaystyle x\ne 3, 7\).

Using that same explicitly stated denominator \(\left(x - 7\right) \left(x - 3\right)\), find the constant term in the numerator of A+B.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{5}{x - 4}\) and \(\displaystyle B=\)\(\displaystyle \frac{3}{x - 9}\). Every operation uses the common original domain \(\displaystyle x\ne 4, 9\).

Using that same explicitly stated denominator \(\left(x - 9\right) \left(x - 4\right)\), find the constant term in the numerator of A+B.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{5}{x - 4}\) and \(\displaystyle B=\)\(\displaystyle \frac{3}{x - 9}\). Every operation uses the common original domain \(\displaystyle x\ne 4, 9\).

Write AB over denominator \(\left(x - 9\right) \left(x - 4\right)\). Find its numerator.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{6}{x - 5}\) and \(\displaystyle B=\)\(\displaystyle \frac{4}{x - 7}\). Every operation uses the common original domain \(\displaystyle x\ne 5, 7\).

Write AB over denominator \(\left(x - 7\right) \left(x - 5\right)\). Find its numerator.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{6}{x - 5}\) and \(\displaystyle B=\)\(\displaystyle \frac{4}{x - 7}\). Every operation uses the common original domain \(\displaystyle x\ne 5, 7\).

Write \(\displaystyle \frac{A}{B}= \frac{K(x- 7)}{x- 5}\). Find K.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle A=\)\(\displaystyle \frac{7}{x - 1}\) and \(\displaystyle B=\)\(\displaystyle \frac{5}{x - 4}\). Every operation uses the common original domain \(\displaystyle x\ne 1, 4\).

Write \(\displaystyle \frac{A}{B}= \frac{K(x- 4)}{x- 1}\). Find K.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{4}{x-3}=\frac{5}{x-8}\) over the real numbers.

Find the valid solution x.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{5}{x-4}=\frac{6}{x-10}\) over the real numbers.

Find the valid solution x.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{5}{x-4}=\frac{6}{x-10}\) over the real numbers.

Find x−4 at the valid solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{6}{x-5}=\frac{7}{x-12}\) over the real numbers.

Find x−5 at the valid solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{6}{x-5}=\frac{7}{x-12}\) over the real numbers.

Find the common value of the two fractions at the solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{2}{x-6}=\frac{3}{x-9}\) over the real numbers.

Find the common value of the two fractions at the solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{2}{x-6}=\frac{3}{x-9}\) over the real numbers.

Find the sum of the two excluded inputs.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(\displaystyle \frac{3}{x-1}=\frac{4}{x-5}\) over the real numbers.

Find the sum of the two excluded inputs.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.