SOLUTION: how do I simplify this and give restrictions? 2x^2 + 7x -15 ----------- - x^2 + x - 20

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Question 82035This question is from textbook Algebra 1 an integraded approach
: how do I simplify this and give restrictions?
2x^2 + 7x -15
-------------
x^2 + x - 20 This question is from textbook Algebra 1 an integraded approach

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you need help with factoring take a look at this solver
%282x%5E2+%2B+7x+-15%29%2F%28x%5E2+%2B+x+-+20%29 Start with the given problem

Factor the numerator

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



Factor the denominator

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




So after factoring we have

%28%282x-3%29%28x%2B5%29%29%2F%28%28x-4%29%28x%2B5%29%29

%28%282x-3%29cross%28%28x%2B5%29%29%29%2F%28%28x-4%29cross%28%28x%2B5%29%29%29 Cancel like terms

%282x-3%29%2F%28x-4%29 Simplify. This is the simplified form.

Now in order for the expression %282x-3%29%2F%28x-4%29
to be equivalent to
%282x%5E2+%2B+7x+-15%29%2F%28x%5E2+%2B+x+-+20%29
We need to find the restrictions. So we need to set the denominators equal to zero:
x-4=0 or x%2B5=0
x=4 or x-5

So the restrictions are that x cannot equal 4 or -5. Notice if we plug in x=4 into the original equation we get

%282%284%29%5E2+%2B+7%284%29+-15%29%2F%284%5E2+%2B+4+-+20%29=45%2F0 which is not possible

the same applies to x=-5

%282%28-5%29%5E2+%2B+7%28-5%29+-15%29%2F%28%28-5%29%5E2+-5+-+20%29=0%2F0 which is also not possible