SOLUTION: Simplify. State any restrictions on the variable. 1. x^2+x-6/x^2+3x 2. 4x^2-25/2x^2+3x-20

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify. State any restrictions on the variable. 1. x^2+x-6/x^2+3x 2. 4x^2-25/2x^2+3x-20       Log On


   

Question 189462: Simplify. State any restrictions on the variable.
1. x^2+x-6/x^2+3x




2. 4x^2-25/2x^2+3x-20

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

# 1



%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 x%5E2%2Bx-6 to get %28x%2B3%29%28x-2%29.


%28%28x%2B3%29%28x-2%29%29%2F%28x%28x%2B3%29%29 Factor x%5E2%2B3x to get x%28x%2B3%29.


%28highlight%28%28x%2B3%29%29%28x-2%29%29%2F%28x%2Ahighlight%28%28x%2B3%29%29%29 Highlight the common terms.


%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 simplifies to %28x-2%29%2Fx.


In other words, %28x%5E2%2Bx-6%29%2F%28x%5E2%2B3x%29=%28x-2%29%2Fx where x%3C%3E-3 or x%3C%3E0