Manipulating Algebraic Fractions

## Manipulating Algebraic Fractions

Simplifying an algebraic fraction involves determining common factors and dividing the numerator and the denominator by those factors.

When calculating with algebraic fractions, the same rules apply as they do for arithmetic fractions: note especially that the denominators must be the same when adding or subtracting.

Often the factors that will be being simplified will be in brackets ie (x + 3). It is always worth factorising quadratic expressions.

## Example 1

Simplify frac((a^2 + 4a + 4))((a^2 - 4))

frac((a^2 + 4a + 4))((a^2 - 4))

= frac((a + 2)(a + 2))((a + 2)(a - 2))

= frac((a + 2))((a - 2))

Answer: frac((a + 2))((a - 2))

## Example 2

Calculate frac((x - 3))((x + 3)) x frac((4x + 12))((2x - 6)).

frac((x - 3))((x + 3)) x frac((4x + 12))((2x - 6))

= frac(4(x - 3)(x + 3))(2(x + 3)(x - 3))

= frac(4)(2) = 2