2.8.1 Algebraic fractions

An algebraic fraction is simply a fraction with algebraic expressions as its numerator and as denominator.

e.g.

\( \frac{2x+1}{3-x} \), \( \frac{x^2+2x+3}{3} \), \( \frac{2}{x-1} \)

To simplify an algebraic fraction

• Factorise fully numerator and denominator

• Cancel common factors/ brackets

Tip:

When you are asked to simplify an algebraic fraction, it is highly likely that one of the factors will be the same on both the numerator and the denominator.

Worked example:

Simplify \( \frac{x^2+5x}{x^2-25} \)

Factorize the numerator and denominator

\( \frac{x(x+5)}{(x-5)(x+5)} \)

Cancel the common brackets

\( =\frac{x}{x-5} \)

\( \frac{x}{x-5} \)

Test yourself:

Question 1:

Simplify \( \frac{x^2-25}{x^2-2x-35} \)

[2]

Question 2:

Simplify \( \frac{4x+6}{2x^2-7x-15} \)

[2]