SOLUTION: Solve 3-(a-14/a+5)=a^2-6/a+5

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Question 315621: Solve
3-(a-14/a+5)=a^2-6/a+5
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Solve
Assume the problem is:
3-%28%28a-14%29%2F%28a%2B5%29%29=%28a%5E2-6%29%2F%28a%2B5%29
:
Multiply by (a+5), results:
3(a+5) - (a-14) = a^2 - 6
:
remove brackets
3a + 15 - a + 14 = a^2 - 6
2a + 29 = a^2 - 6
Combine on the right
0 = a^2 - 2a - 6 - 29
:
A quadratic equation
a^2 - 2a - 35 = 0
:
Factors to
(a-7)(a+5) = 0
:
Two solutions
a = -5, not a solution, makes the denominator 0
and
a = 7
:
Check in original problem:
3-%28%28a-14%29%2F%28a%2B5%29%29=%28a%5E2-6%29%2F%28a%2B5%29
:
3-%28%287-14%29%2F%287%2B5%29%29=%287%5E2-6%29%2F%287%2B5%29
:
3-%28%28-7%29%29%2F%2812%29%29=%2849-6%29%2F%2812%29
:
%2836%2F12%29+%2B+%287%2F%2812%29%29=%2843%29%2F%2812%29