Question

How do you combine `\frac { 5x } { x ^ { 2} - 9} + \frac { 2x } { x ^ { 2} + 2x - 3} - \frac { 2} { x ^ { 2} - 6x + 9}` into one fraction?

Answer 1

`=(5x^2 -15x+6)/((x+3)(x-3)(x-1))`

Explanation:

With algebraic fractions, factorise first.

`(5x)/((x+3)(x-3))+ (2x)/((x+3)(x-1)) - 2/((x-3)(x-3))`

Now find the common denominator.
Each fraction must be multiplied by the factor it is missing.

`= (5x(x-1) +2x(x-3)-2(x+3)(x-1))/((x+3)(x-3)(x-1))`

`= (5x^2-5x +2x^2-6x-2(x^2+2x-3))/((x+3)(x-3)(x-1))`

`= (5x^2-5x +2x^2-6x-2x^2-4x+6)/((x+3)(x-3)(x-1))`

`=(5x^2 -15x+6)/((x+3)(x-3)(x-1))`