SOLUTION: If (a) does not equal (b), solve for x in terms of (a) and (b): ax+b(ax-b)=a(bx-a)-bx

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Question 72678: If (a) does not equal (b), solve for x in terms of (a) and (b):
ax+b(ax-b)=a(bx-a)-bx
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
ax%2Bb%28ax-b%29+=+a%28bx-a%29-bx Expand the parentheses.
ax%2Babx-b%5E2+=+abx-a%5E2-bx Simplify. Subtract abx from both sides.
ax-b%5E2+=+-a%5E2-bx Add a%5E2 to both sides.
a%5E2-b%5E2%2Bax+=+-bx Add bx to both sides.
a%5E2-b%5E2%2Bax%2Bbx+=+0 Simplify.
%28a%5E2-b%5E2%29%2Bx%28a%2Bb%29+=+0 Subtract %28a%5E2-b%5E2%29 from both sides.
x%28a%2Bb%29+=+-%28a%5E2-b%5E2%29 Divide both sides by %28a%2Bb%29
x+=+-%28a%5E2-b%5E2%29%2F%28a%2Bb%29 Factor the numerator.
x+=+-%28%28a%2Bb%29%28a-b%29%29%2F%28a%2Bb%29 Cancel the%28a%2Bb%29
x+=+-%28a-b%29
x+=+b-a