SOLUTION: Rational expression solve and check (X+2)/(2x+2)=(3x+2)/(3x-2)

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Question 1039626: Rational expression solve and check
(X+2)/(2x+2)=(3x+2)/(3x-2)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply both sides by %282x%2B2%29%283x-2%29, the simplest or lowest common denominator. This gives %28x%2B2%29%283x-2%29=%283x%2B2%29%282x%2B2%29

3x%5E2%2B6x-2x-4=6x%5E2%2B2x%2B6x%2B4

4x-4=3x%5E2%2B8x%2B4

0=3x%5E2%2B4x%2B8, but the discriminant is 4%5E2-4%2A3%2A8=-80, a negative numbers. NO REAL SOLUTIONS. Do you want Complex solutions?


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"Yes"...

You should both check the discussion for this in YOUR textbook, and also review this couple of lessons:
Solve Quadratic Equation using Completing The Square
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What is Completing The Square

Going directly to the general solution formula for a quadratic equation,
x=%28-8%2B-+sqrt%28-80%29%29%2F%282%2A3%29

x=%28-8%2B-+sqrt%28-1%2A2%2A2%2A2%2A2%2A5%29%29%2F%282%2A3%29

x=%28-8%2B-+4i%2Asqrt%285%29%29%2F%282%2A3%29

highlight%28x=%28-4%2B-+2i%2Asqrt%285%29%29%2F3%29
Those will be no trouble for the denominator because the solutions will not make denominators become 0.