SOLUTION: Simplify. State any restrictions on the variable[thanks for your wonderful help] x^2+x-6/x^2+3x 4x^2-25/2x^2+3x-20

Algebra ->  Rational-functions -> SOLUTION: Simplify. State any restrictions on the variable[thanks for your wonderful help] x^2+x-6/x^2+3x 4x^2-25/2x^2+3x-20      Log On


   

Question 188590: Simplify. State any restrictions on the variable[thanks for your wonderful help]
x^2+x-6/x^2+3x


4x^2-25/2x^2+3x-20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2Bx-6%29%2F%28x%5E2%2B3x%29 Start with the given expression


%28%28x%2B3%29%28x-2%29%29%2F%28x%5E2%2B3x%29 Factor the numerator


%28%28x%2B3%29%28x-2%29%29%2F%28x%28x%2B3%29%29 Factor the denominator


%28cross%28%28x%2B3%29%29%28x-2%29%29%2F%28x%2Across%28%28x%2B3%29%29%29 Cancel out the common terms.


%28x-2%29%2Fx Simplify


So %28x%5E2%2Bx-6%29%2F%28x%5E2%2B3x%29=%28x-2%29%2Fx where x%3C%3E0 or x%3C%3E-3 (these are the restrictions). Note: These restrictions are made to avoid division by zero.



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%284x%5E2-25%29%2F%282x%5E2%2B3x-20%29 Start with the given expression


%28%282x%2B5%29%282x-5%29%29%2F%28x%5E2%2B3x%29 Factor the numerator


%28%282x%2B5%29%282x-5%29%29%2F%28%28x%2B4%29%282x-5%29%29 Factor the denominator


%28%282x%2B5%29cross%28%282x-5%29%29%29%2F%28%28x%2B4%29cross%28%282x-5%29%29%29 Cancel out the common terms.


%282x%2B5%29%2F%28x%2B4%29 Simplify


So %284x%5E2-25%29%2F%282x%5E2%2B3x-20%29=%282x%2B5%29%2F%28x%2B4%29 where x%3C%3E-4 or x%3C%3E5%2F2 (these are the restrictions). Note: These restrictions are made to avoid division by zero.