SOLUTION: Solve for x : 1+ 3x/(x+5)(x-2) = 2/(x-5) + 3/(x-2)

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Question 119141: Solve for x : 1+ 3x/(x+5)(x-2) = 2/(x-5) + 3/(x-2)
Answer by jim_thompson5910(28555) About Me  (Show Source):
You can put this solution on YOUR website!

1%2B%283x%29%2F%28x%2B5%29%28x-2%29=%282%29%2F%28x-5%29%2B%283%29%2F%28x-2%29 Start with the given equation


Multiply both sides by the LCD %28x%2B5%29%28x-2%29%28x-5%29. Doing this will eliminate every fraction.


Distribute and multiply. Notice every denominator has been canceled out.



Foil



%28x%5E2%2B3x-10%29%28x-5%29%2B3x%5E2-15x=2x%5E2%2B6x-20%2B3x%5E2-75 Distribute



x%5E3%2B3x%5E2-10x-5x%5E2-15x%2B25%2B3x%5E2-15x=2x%5E2%2B6x-20%2B3x%5E2-75 Expand



x%5E3%2Bx%5E2-40x%2B50=5x%5E2%2B6x-95 Combine like terms



x%5E3%2Bx%5E2-40x%2B50-5x%5E2-6x%2B95=0 Get all of the terms to the left side



x%5E3-4x%5E2-46x%2B145=0 Get all of the terms to the left side



Now use your calculator to find the roots of the cubic. So the roots are


x=-6.503, x=2.954, or x=7.549