SOLUTION: x+1/x+2+1/x / x/x+2=1/x^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x+1/x+2+1/x / x/x+2=1/x^2      Log On


   

Question 148530This question is from textbook Algebra 1 california edition
: x+1/x+2+1/x / x/x+2=1/x^2 This question is from textbook Algebra 1 california edition

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
If I imagine this problem correctly, it looks like this:
%28%28%28x%2B1%29%2F%28x%2B2%29%29%2B%281%2Fx%29%29%2F%28x%2F%28x%2B2%29%29=1%2Fx%5E2

First add x+1/x+2 and 1/x. First get a common denominator: x(x+2). So multiply x+1/x+2 by x/x and 1/x by x+2/x+2.



Simplify it


becomes (in the numerators)

Add in the numerators and simplify
%28%28x%5E2%2B2x%2B2%29%2F%28x%5E2%2B2x%29%29%2F%28x%2F%28x%2B2%29%29=1%2Fx%5E2

Flip the second fraction
%28%28x%5E2%2B2x%2B2%29%2F%28x%5E2%2B2x%29%29%28%28x%2B2%29%2Fx%29=1%2Fx%5E2

Multiply across
%28x%5E3%2B2x%5E2%2B2x%2B2x%5E2%2B4x%2B4%29%2F%28x%5E3%2B2x%5E2%29

Add the terms

%28x%5E3%2B4x%5E2%2B6x%2B4%29%2F%28x%5E3%2B2x%5E2%29

Group
%28%28x%5E3%2B4x%5E2%29%2B%286x%2B4%29%29%2F%28%28x%5E3%2B2x%5E2%29%29

Factor

%28x%5E2%28x%2B4%29%2B2%283x%2B2%29%29%2F%28x%5E2%28x%2B2%29%29

Cancel out the x%5E2's

%28%28x%2B4%29%2B2%283x%2B2%29%29%2F%28x%2B2%29