SOLUTION: Determine solution set x+5/x-4>3x+2/2x+1

Question 150259: Determine solution set x+5/x-4>3x+2/2x+1
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
(x+5)/(x-4)>(3x+2)/(2x+1)
(x+5)(2x+1)=(3x+2)(x-4) turn it into an equality
2x^2+11x+5=3x^2-10x-8
x-21x-13=0 Subtract the left side from the right.
x=-.6018..., x=21.6018...
x cannot be 4 or -0.5 because there would be division by zero in the original equation. (vertical asymptotes)
You now have 4 points around which to test: -.6018, -.5, 4, and 21.6018
Try numbers larger and smaller than these numbers for x to see if the left side is larger than the right.
-1 no
-0.6 yes
0 no
5 yes
25 no
.
X(.6018,-.5)U(4,21.6018) answer
.
On the graph below the left side of the equation is the red line and the right, the green.
.
Ed
.

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