Question

How do you simplify `(x^2-5)/(x^2 +5x - 14)-((x+3)/(x+7))`?

Answer 1

Here's how you could simplify this expression.

Explanation:

Start by writing out your starting expression

`(x^2 - 5)/(x^2 + 5x - 14) - (x+3)/(x+7)`

Next, factor the denominator of the first fraction

`x^2 + 5x - 14`

`x^2 + 7x - 2x - 14`

`x(x-2) + 7(x-2)`

`(x-2)(x+7)`

Your expression is thus equivalent to

`(x^2 - 5)/[(x-2) * (x+7)] - (x+3)/(x+7)`

Since you have to subtract two fractions, you need to find the commonon denominator first. To do that, multiply the second fraction by `(x-2)/(x-2)`

`(x^2 - 5)/[(x - 2) * (x + 7)] - [(x+3) * (x-2)]/[(x-2) * (x + 7)]`

This will get you

`(x^2 - 5 - (x+3)(x-2)]/[(x-2)(x+7)]`

`(cancel(x^2) - 5 - cancel(x^2) -x + 6)/[(x-2)(x+7)] = color(green)((1-x)/[(x-2)(x+7)])`