SOLUTION: Solve the equation. 24/(x-2)+24/(x+2)=5

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Question 173802This question is from textbook Introductory Algebra
: Solve the equation.
24/(x-2)+24/(x+2)=5 This question is from textbook Introductory Algebra

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the CD, common denominator (x-2)*(x+2), multiply thru by it
24(x+2) + 24(x-2) = 5*(x+2)*(x-2)
(24x+48 + 24x - 48) = 5x^2 - 20
48x = 5x^2 - 20
5x^2 - 48x - 20 = 0
(5x+2)*(x-10) = 0
x = 10
x = -2/5
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Here's a graph
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-48x%2B-20+=+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=%28-48%29%5E2-4%2A5%2A-20=2704.

Discriminant d=2704 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--48%2B-sqrt%28+2704+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+2704+%29%29%2F2%5C5+=+10
x%5B2%5D+=+%28-%28-48%29-sqrt%28+2704+%29%29%2F2%5C5+=+-0.4

Quadratic expression 5x%5E2%2B-48x%2B-20 can be factored:
5x%5E2%2B-48x%2B-20+=+%28x-10%29%2A%28x--0.4%29
Again, the answer is: 10, -0.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-48%2Ax%2B-20+%29