Algebraic Fractions

Simplify algebraic fractions by factorising where possible and then cancelling terms on the top and bottom.

Multiplication

To multiply two algebraic fractions together, multiply the tops and bottoms separately.

Division

To divide by an algebraic fraction, turn it upside down and then multiply as usual.

Algebraic Fractions - Addition and Subtraction

To add (or subtract) algebraic fractions together, work out the common denominator and rewrite each so they all share the denominator. Then add (or subtract) the numerators.

Example

The common denominator here is x(1 + x).

Step 1

Multiply the top and bottom of middle term by (1 + x).
Multiply the top and bottom of the last term by x.
The denominators (bottom parts) are now all the same.

Step 2

Add the numerators (top parts) together and keep the common denominator (bottom part).

Test yourself on Algebraic Fractions

How do we divide 2 fractions?
What is $\frac{x+1}{2x-1} \times \frac{x-1}{x+6}$ ?
What is $\frac{x+1}{2x-1} \div \frac{x-1}{x+6}$ ?
What is $\frac{3x+3}{2x-7} \times \frac{x-4}{x+2}$ ?
What is $\frac{2x-7}{3x+3} \div \frac{x-4}{x+2}$ ?

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