SOLUTION: I can not find an answer to this, I tried to factor but that did not turn out right. Please help. (x+4)/(6x^2+5x-6)+(x)/(2x+3)= (x)/(3x-2)

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: I can not find an answer to this, I tried to factor but that did not turn out right. Please help. (x+4)/(6x^2+5x-6)+(x)/(2x+3)= (x)/(3x-2)      Log On

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Question 7751: I can not find an answer to this, I tried to factor but that did not turn out right. Please help.
(x+4)/(6x^2+5x-6)+(x)/(2x+3)= (x)/(3x-2)
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, here we go!
%28x%2B4%29%2F%286x%5E2%2B5x-6%29+%2B+x%2F%282x%2B3%29+=+x%2F%283x-2%29 Factor the denominator of the 1st fraction.
%28x%2B4%29%2F%282x%2B3%29%283x-2%29+%2B+x%2F%282x%2B3%29+=+x%2F%283x-2%29 Add the two fractions on the left side. Common denominator is (2x+3)(3x-2), so multiply the 2nd fraction by (3x-2)/(3x-2)
%28x%2B4%29%2F%282x%2B3%29%283x-2%29+%2B+%283x-2%29%28x%29%2F%282x%2B3%29%283x-2%29+=+x%2F%283x-2%29 Add 'em up.
%28x%2B4%2B%283x-2%29x%29%2F%282x%2B3%29%283x-2%29+=+x%2F%283x-2%29 Simplify the left side.
%283x%5E2+-+x+%2B+4%29%2F%282x%2B3%29%283x-2%29+=+x%2F%283x-2%29 Multiply both sides by (3x-2)
%283x%5E2+-+x+%2B+4%29%2F%282x%2B3%29+=+x Multiply both sides by (2x+3)
3x%5E2+-+x+%2B+4+=+2x%5E2+%2B+3x Simplify and set equal to zero.
x%5E2+-4x+%2B+4+=+0 Solve the quadratic equation by factoring.
%28x-2%29%28x-2%29+=+0 Apply the zero product principle.
x-2 = 0, then x = 2
The solution is: a double root; x = 2
Check:
%282%2B4%29%2F%286%282%5E2%29%2B5%282%29-6%29%2B+2%2F%282%282%29%2B3%29+=+2%2F%283%282%29-2%29
6%2F28+%2B+2%2F7+=+2%2F4
6%2F28+%2B+8%2F28+=+14%2F28
%286%2B8%29%2F28+=+14%2F28
14%2F28+=+14%2F28