Question

Rational expression,, please explain!

I understand mostly, but the subtraction sign throws me off... ​

Answer 1

x = 2

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:

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

Then, create a common denominator on the right:

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

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

Put everything on one side:

`0 = (2(x - 2) - 1(x + 3))/((x+3)(x-2)) - (3)/((x + 3)(x - 2))`

`0 = (2(x - 2) - 1(x + 3) - 3)/((x+3)(x-2))`

`0 = (2x - 4 - x - 3 - 3)/((x+3)(x-2))`

`0 = (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.