SOLUTION: (1/(x+2))+(2/(x-3))<=1 here is my work: ((x-3)+2(x+2)-((x+2)(x-3)))/((x+2)(x-3))<=0 you then simplify to get: (-x^2 +2x +7)/((x+2)(x-3))<=0 but when you use the quadratic eq

Algebra ->  Inequalities -> SOLUTION: (1/(x+2))+(2/(x-3))<=1 here is my work: ((x-3)+2(x+2)-((x+2)(x-3)))/((x+2)(x-3))<=0 you then simplify to get: (-x^2 +2x +7)/((x+2)(x-3))<=0 but when you use the quadratic eq      Log On


   

Question 32056: (1/(x+2))+(2/(x-3))<=1
here is my work:
((x-3)+2(x+2)-((x+2)(x-3)))/((x+2)(x-3))<=0
you then simplify to get:
(-x^2 +2x +7)/((x+2)(x-3))<=0
but when you use the quadratic equation it is very ugly.
Thank you,
Alexus
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see:
%281%2F%28x%2B2%29%29%2B%282%2F%28x-3%29%29%3C=1 Add the fractions on the left.
%28%28x-3%29%2B2%28x%2B2%29%29%2F%28%28x%2B2%29%28x-3%29%29+%3C=1 Multiply both sides by%28x%2B2%29%28x-3%29
x-3%2B2x%2B4+%3C=+%28x%2B2%29%28x-3%29 Simplify.
3x%2B1%3C=x%5E2-x-6 Subtract%283x%2B1%29 from both sides.
0%3C=x%5E2-4x-7 or x%5E2-4x-7%3E=0
Begin by solving the quadratic equationx%5E2-4x-7+=+0Solve for x using the quadratic formulax=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a.
x=%284%2B-sqrt%2816%2B28%29%29%2F2 Simplify.
x=%284%2B-sqrt%2844%29%29%2F2
x=%284%2B-2sqrt%2811%29%29%2F2
x=2%2B-sqrt%2811%29
The x-intercepts are:
x+=+2%2Bsqrt%2811%29
x+=+2-sqrt%2811%29
But since we are solving:x%5E2-4x-7%3E=0 we are looking for x-values with positve y-values. Looking at the graph of the quadratic equation:
graph%28300%2C200%2C-3%2C6%2C-12%2C5%2Cx%5E2-4x-7%29
The solution set is x%3C=2-sqrt%2811%29orx%3E=2%2Bsqrt%2811%29