SOLUTION: Please help me solve this: {{{(3x^2+9x-30)/(3x^2-75)}}}

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Question 78332: Please help me solve this:
%283x%5E2%2B9x-30%29%2F%283x%5E2-75%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: check out this solver to help you factor

Factor the numerator

ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .




Now factor the denominator


ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .





So the expression %283x%5E2%2B9x-30%29%2F%283x%5E2-75%29 factors to

%28%283x-6%29%28x%2B5%29%29%2F%28%283x%2B15%29%28x-5%29%29

%28%283x-6%29%28x%2B5%29%29%2F%283%28x%2B5%29%28x-5%29%29 Factor out a 3 in the denominator

%28%283x-6%29cross%28%28x%2B5%29%29%29%2F%283cross%28%28x%2B5%29%29%28x-5%29%29 Notice these terms cancel

%283x-6%29%2F%283%28x-5%29%29

3%28x-2%29%2F%283%28x-5%29%29 Factor out a 3 in the numerator

cross%283%29%28x-2%29%2F%28cross%283%29%28x-5%29%29 Notice the 3's cancel

%28x-2%29%2F%28x-5%29 This is the simplified answer