Operations with algebraic fractions · Short practice
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Operations with algebraic fractions — objective 1
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.
Fresh review variant
Operations with algebraic fractions — objective 1
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.
Method
Operations with algebraic fractions — objective 2
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.
Fresh review variant
Operations with algebraic fractions — objective 2
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.
Apply
Operations with algebraic fractions — objective 3
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.
Fresh review variant
Operations with algebraic fractions — objective 3
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.
Check understanding
Operations with algebraic fractions — objective 4
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.
Fresh review variant
Operations with algebraic fractions — objective 4
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.