How do you simplify $\frac{3 x - 2}{x + 3} + \frac{7}{x^{2} - x - 12}$ $(3x-2)/(x+3)+7/(x^2-x-12)$ ?

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Answer 1 · 2017-07-02T11:31:02

$\frac{(x - 3) (3 x - 5)}{(x + 3) (x - 4)}$ $((x-3)(3x-5))/((x+3)(x-4))$

First, factor out the denominator of the right hand term

$\frac{3 x - 2}{x + 3} + \frac{7}{(x + 3) (x - 4)}$ $(3x-2)/(x+3)+7/((x+3)(x-4))$

Next multiply the numerator and denominator of the first term by $(x - 4)$ $(x-4)$ in order to get a common denominator.

$\frac{x - 4}{x - 4} \frac{3 x - 2}{x + 3} + \frac{7}{(x + 3) (x - 4)}$ $(x-4)/(x-4)(3x-2)/(x+3)+7/((x+3)(x-4))$

Combine the two fractions.

$\frac{(x - 4) (3 x - 2) + 7}{(x + 3) (x - 4)}$ $((x-4)(3x-2)+7)/((x+3)(x-4))$

Expand the numerator

$\frac{3 x^{2} - 12 x - 2 x + 8 + 7}{(x + 3) (x - 4)}$ $(3x^2-12x-2x+8+7)/((x+3)(x-4))$

Simplify the numerator

$\frac{3 x^{2} - 14 x + 15}{(x + 3) (x - 4)}$ $(3x^2-14x+15)/((x+3)(x-4))$

Factor the numerator

$\frac{(x - 3) (3 x - 5)}{(x + 3) (x - 4)}$ $((x-3)(3x-5))/((x+3)(x-4))$

How do you simplify 3x−2x+3+7x2−x−12(3x-2)/(x+3)+7/(x^2-x-12)?