SOLUTION: x^2-2x+3/x+1 is less than or equal to 1. I know i have to get 1 on the other side so i will end up with x^2-2x+3/x+1 - 1 is less than or equal to 0. Other than that I don't kno

Algebra ->  Systems-of-equations -> SOLUTION: x^2-2x+3/x+1 is less than or equal to 1. I know i have to get 1 on the other side so i will end up with x^2-2x+3/x+1 - 1 is less than or equal to 0. Other than that I don't kno      Log On


   

Question 1121666: x^2-2x+3/x+1 is less than or equal to 1.
I know i have to get 1 on the other side so i will end up with x^2-2x+3/x+1 - 1 is less than or equal to 0.
Other than that I don't know what to do.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-2x%2B3%29%2F%28x%2B1%29+%3C=+1......add -1 to both sides
%28x%5E2-2x%2B3%29%2F%28x%2B1%29-1+%3C=+1-1
%28x%5E2-2x%2B3%29%2F%28x%2B1%29-1+%3C=+0....now get a rid of denominator on the left side; multiply both sides by x%2B1

%28%28x%2B1%29%28x%5E2-2x%2B3%29%29%2F%28x%2B1%29-1%28x%2B1%29+%3C=+0%28x%2B1%29

%28cross%28%28x%2B1%29%29%28x%5E2-2x%2B3%29%29%2Fcross%28%28x%2B1%29%29-1%28x%2B1%29+%3C=+0

%28x%5E2-2x%2B3%29-1%28x%2B1%29+%3C=+0%29

x%5E2-2x%2B3-x-1+%3C=+0%29

x%5E2-3x%2B2+%3C=+0%29......factor completely; write -3x as -x-2x

x%5E2-x-2x%2B2+%3C=+0%29....group

%28x%5E2-x%29-%282x-2%29+%3C=+0%29....factor

x%28x-1%29-2%28x-1%29+%3C=+0%29

%28x-2%29%28x-1%29+%3C=+0%29
solutions:
if %28x-2%29+%3C=+0%29 => x+%3C=+2%29
if %28x-1%29+%3C=+0%29 => x+%3C=+1%29