Answer to Question #3977 in Algebra for Brady

Question

Simplify (x^2+x+7)/(x-3)(x+4) - (x^2+3)/(x^2+x-12) I've tried it multiple times but I just can't seem to get it right!

Answer 1

<img src="/cgi-bin/mimetex.cgi?\frac{x^2+x+7}{(x-3)(x+4)}-\frac{x^2+3}{x^2+x-12} = \frac{x^2+x+7}{(x-3)(x+4)}-\frac{x^2+3}{(x-3)(x+4)} = \frac{x^2+x+7-x^2-3}{(x-3)(x+4)} = \frac{x+4}{(x-3)(x+4)} = \frac{1}{x-3}" title="\frac{x^2+x+7}{(x-3)(x+4)}-\frac{x^2+3}{x^2+x-12} = \frac{x^2+x+7}{(x-3)(x+4)}-\frac{x^2+3}{(x-3)(x+4)} = \frac{x^2+x+7-x^2-3}{(x-3)(x+4)} = \frac{x+4}{(x-3)(x+4)} = \frac{1}{x-3}">