SOLUTION: Hi, can you please help me with this problem as well. Thank you! Solve. (x-a)/(a-b) - (x+b)/(a+b) = (2a(x-b))/(a^2-b^2) + (a-b)/(a+b)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hi, can you please help me with this problem as well. Thank you! Solve. (x-a)/(a-b) - (x+b)/(a+b) = (2a(x-b))/(a^2-b^2) + (a-b)/(a+b)      Log On


   

Question 1084643: Hi, can you please help me with this problem as well.
Thank you!
Solve. (x-a)/(a-b) - (x+b)/(a+b) = (2a(x-b))/(a^2-b^2) + (a-b)/(a+b)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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Factor aČ-bČ

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To avoid denominators equaling 0, we must have the restrictions
that a ≠ b and a ≠ -b

Multiply through by LCD of (a-b)(a+b)

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%28ax%2Bbx-a%5E2-ab%29+-+%28ax-bx%2Bab-b%5E2%29%29%22%22=%22%222ax-2ab+%2B+%28a%5E2-ab-ab%2Bb%5E2%29

ax%2Bbx-a%5E2-ab+-+ax%2Bbx-ab%2Bb%5E2%22%22=%22%222ax-2ab+%2B+a%5E2-ab-ab%2Bb%5E2

-a%5E2+%2B+b%5E2+%2B+2bx%22%22=%22%22a%5E2+-+4ab+%2B+2ax+%2B+b%5E2 

-2ax+%2B+2bx%22%22=%22%222a%5E2+-+2ab

Divide through by -2

ax+-+bx%22%22=%22%22-a%5E2+%2B+ab

x%28a+-+b%29%22%22=%22%22-a%28a+-+b%29

x%22%22=%22%22-a%28a+-+b%29%2F%28a-b%29

x%22%22=%22%22%28-a%28cross%28a-b%29+%29%29%2F%28+cross%28a-b%29+%29

x%22%22=%22%22-a

Edwin