SOLUTION: Could you please show me how to solve this: {{{3 -(a-5)/(a+5) = (a^2-15)/(a+5) }}} Thank you in advance for your efforts.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Could you please show me how to solve this: {{{3 -(a-5)/(a+5) = (a^2-15)/(a+5) }}} Thank you in advance for your efforts.       Log On


   

Question 193641: Could you please show me how to solve this: 3+-%28a-5%29%2F%28a%2B5%29+=+%28a%5E2-15%29%2F%28a%2B5%29+
Thank you in advance for your efforts.

Found 2 solutions by Earlsdon, Alan3354:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for a:
3-%28%28a-5%29%2F%28a%2B5%29%29+=+%28a%5E2-15%29%2F%28a%2B5%29 Simplify the left side.
%283%28a%2B5%29-%28a-5%29%29%2F%28a%2B5%29+=+%28a%5E2-15%29%2F%28a%2B5%29
%283a%2B15-a%2B5%29%2F%28a%2B5%29+=+%28a%5E2-15%29%2F%28a%2B5%29
%282a%2B20%29%2F%28a%2B5%29+=+%28a%5E2-15%29%2F%28a%2B5%29 Multiply both sides by (a+5).
2a%2B20+=+a%5E2-15 Rearrange this to form a quadratic equation in standard form.
a%5E2-2a-35+=+0 Factor.
%28a-7%29%28a%2B5%29+=+0
a+=+7 or a+=+-5 But...if we substitute a = -5 into the original equation then we have division by zero which, of course, is a no-no! So a = -5 is and excluded solution.
The acceptable solution is:
highlight%28a+=+7%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please show me how to solve this: 3+-%28a-5%29%2F%28a%2B5%29+=+%28a%5E2-15%29%2F%28a%2B5%29+
----------------
Multiply by (a+5)
3%28a%2B5%29+-%28a-5%29+=+a%5E2-15
3a%2B15+-a%2B5+=+a%5E2-15
2a%2B20+=+a%5E2-15
a%5E2+-+2a+-+35+=+0
(a+5)*(a-7) = 0
a = -5
a = 7