SOLUTION: Solve each rational equation. Complex numbers are very confusing for me. 4x over x+3 minus 12 over x-3 = 4x^2+36 over x^2-9 Thank you so much , I greatly appreciate the h

Question 1039438: Solve each rational equation. Complex numbers are very confusing for me.
4x over x+3
minus
12 over x-3
=
4x^2+36 over x^2-9
Thank you so much , I greatly appreciate the help
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
4x/(x+3) - 12/(x-3)=4x^2+36/x^2-9
common denominator is (x+3)(x-3) or x^2-9. Multiply each term in the equation by that.
x+3 will divide into that (x-3) times and x-3 will divide into that (x+3) times.
4x(x-3)-12(x+3)=4x^2+36, since the x^2-9 will cancel on the right.
distribute
4x^2-12x-12x-36=4x^2+36
collect terms
4x^2-12x-12x-36=4x^2+36
the 4x^2 cancels.
-24x-36=36
0=24x+72
divide by 24
0=x+3
x= -3
check
the first has a denominator of 0. No solution.

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