SOLUTION: Solve 1/(x-a)+1/(x+a)=2/(x-1). The answer is x=a^2 but I don't know how to get that. Thank you!

Algebra ->  Linear-equations -> SOLUTION: Solve 1/(x-a)+1/(x+a)=2/(x-1). The answer is x=a^2 but I don't know how to get that. Thank you!      Log On


   

Question 979682: Solve 1/(x-a)+1/(x+a)=2/(x-1). The answer is x=a^2 but I don't know how to get that. Thank you!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x-a%29%2B1%2F%28x%2Ba%29%22%22=%22%222%2F%28x-1%29

Clear of fractions.  Multiply through by LCD = (x-a)(x+a)(x-1):

%28x%2Ba%29%28x-1%29%2B%28x-a%29%28x-1%29%22%22=%22%222%28x-a%29%28x%2Ba%29

Use FOIL three times:

x%5E2-x%2Bax-a%2Bx%5E2-x-ax%2Ba%22%22=%22%222%28x%5E2%2Bax-ax-a%5E2%29

Combine like terms:

2x%5E2-2x%22%22=%22%222%28x%5E2-a%5E2%29

Distribute to remove parentheses on the right:

2x%5E2-2x%22%22=%22%222x%5E2-2a%5E2

Add -2x² to both sides:

-2x%22%22=%22%22-2a%5E2

Divide both sides by -2:

x%22%22=%22%22a%5E2

Edwin