Question

rational expression,, please explain!
I understand mostly, but the subtraction sign throws me off... ​

Answer 1

Answer:

x = 2

Step-by-step explanation:

What is needed to solve this equation is a common denominator. With a common denominator, you can get rid of subtracted fractions.

First, factor the denominator on the left side of the equation:

$\frac{3}{(x + 3)(x - 2)} = \frac{2}{x+3} - \frac{1}{x-2}$

Then, create a common denominator on the right:

$\frac{3}{(x + 3)(x - 2)} = \frac{2}{x+3}(\frac{x-2}{x-2}) - \frac{1}{x-2}(\frac{x+3}{x+3})$

$\frac{3}{(x + 3)(x - 2)} = \frac{2(x - 2) - 1(x + 3)}{(x+3)(x-2)}$

Put everything on one side:

$0 = \frac{2(x - 2) - 1(x + 3)}{(x+3)(x-2)} - \frac{3}{(x + 3)(x - 2)}$

$0 = \frac{2(x - 2) - 1(x + 3) - 3}{(x+3)(x-2)}$

$0 = \frac{2x - 4 - x - 3 - 3}{(x+3)(x-2)}$

$0 = \frac{x - 10}{(x+3)(x-2)}$

set each term equal to zero:

x - 10 = 0

x = 10

x + 3 = 0

x = -3

x - 2 = 0

x = 2 is the answer, since it is the only answer which is listed in the multiple choice question.