SOLUTION: {{{(2x/(x+4))=(3/(x-1))}}}

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Question 292159: %282x%2F%28x%2B4%29%29=%283%2F%28x-1%29%29
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2F%28x%2B4%29%29=%283%2F%28x-1%29%29 multiply diagnally
2x%28x-1%29=3%28x%2B4%29distribute
2x%5E2-2x=3x%2B12 subtract 3x and 12
2x%5E2-2x-3x-12=0add like terms
2x%5E2-5x-12=0 quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-5x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A2%2A-12=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+121+%29%29%2F2%5C2+=+4
x%5B2%5D+=+%28-%28-5%29-sqrt%28+121+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2x%5E2%2B-5x%2B-12 can be factored:
2x%5E2%2B-5x%2B-12+=+2%28x-4%29%2A%28x--1.5%29
Again, the answer is: 4, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-12+%29