SOLUTION: I NEED TO KNOW HOW TO DO THESE!!! (x+4) /(6x^2+5x-6) + x/(2x+3)= x/ (3x-2) SOLVE FOR X

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Question 3984: I NEED TO KNOW HOW TO DO THESE!!!
(x+4) /(6x^2+5x-6) + x/(2x+3)= x/ (3x-2)
SOLVE FOR X
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B4%29%2F%286x%5E2%2B5x-6%29+%2B+x%2F%282x%2B3%29+=+x%2F%283x-2%29
%28x%2B4%29%2F%28%283x-2%29%282x%2B3%29%29+%2B+x%2F%282x%2B3%29+=+x%2F%283x-2%29

Now multiply every term by (3x-2)(2x+3):

%28%28x%2B4%29%283x-2%29%282x%2B3%29%29%2F%28%283x-2%29%282x%2B3%29%29+%2B+x%28%283x-2%29%282x%2B3%29%29%2F%282x%2B3%29+=+x%28%283x-2%29%282x%2B3%29%29%2F%283x-2%29

Now we can cancel terms:

%28x%2B4%29+%2B+x%283x-2%29+=+x%282x%2B3%29
x%2B4+%2B+3x%5E2-2x+=+2x%5E2%2B3x
x%5E2+-+4x+%2B+4+=+0

(x-2)(x-2) = 0

so x=2.

I haven't checked, but put x=2 into the original Righthand side and lefthand side and the answer should be the same number.

jon.