SOLUTION: Homework example. Please help me understand and show me how to solve this complex fraction. Thanks! 3/x-2 + 21/x^2-4 = 14/x+2

Question 78353: Homework example. Please help me understand and show me how to solve this complex fraction. Thanks!
3/x-2 + 21/x^2-4 = 14/x+2

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I assume you mean; (a few brackets would help remove all doubt)
:
+ =
:
Notice that (x^2 - 4) is the difference of squares, can be factored to:
+ =
:
If we multiply thru by (x-2)(x+2) we have:
:
3(x+2) + 21 = 14(x-2)
:
Multiply what's inside the brackets and do some basic algebra:
3x + 6 + 21 = 14x - 28
3x + 27 = 14x - 28
3x - 14x = -28 - 27
-11x = -55
x = -55/-11
x = +5
:
:
Check our solution of x=5 for equality in the original equation:
+ =
:
+ = ; confirms our solution
:
How about this? Did you understand what went on here?

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