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Rational expression,, please explain!

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

Rational expression,, please explain! I understand mostly, but the subtraction sign-example-1
User Kool
by
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1 Answer

4 votes

Answer:

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.

User Jason Fulghum
by
9.1k points

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