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

1 Answer
Jul 25, 2015

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)])