SOLUTION: Could someone show me how to solve this? It'll help me study for me exam since I missed this section's notes and have no idea on how to do this problem. As always, help is always a

Algebra ->  Rational-functions -> SOLUTION: Could someone show me how to solve this? It'll help me study for me exam since I missed this section's notes and have no idea on how to do this problem. As always, help is always a      Log On


   

Question 72741: Could someone show me how to solve this? It'll help me study for me exam since I missed this section's notes and have no idea on how to do this problem. As always, help is always appreciated. Thank you. :)

Solve +%28x%29%2F%28x-2%29-%283x%29%2F%284-x%29=%28-2%29%28x-6%29%2F%28x%5E2-6x%2B8%29+
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x)/(x-2)-(3x)/(4-x)=(-2)(x-6)/(x^2-6x+8)
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If you factor the last denominator you get (x-4)(x-2)
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The 2nd fraction can be re-written as +(3x)/(x-4)
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Now the problem looks like:
(x)/(x-2)+(3x)/(x-4)=(-2)(x-6)/[(x-4)(x-2)]
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The least common multiple (lcm) of the denominators is (x-2)(x-4)
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Multiply thru by the lcm to get rid of the denominators.
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[x(x-4)] + (3x)(x-2) = -2(x-6)
x^2-4x + 3x^2-6x = -2x+12
4x^2 - 8x -12 = 0
x^2 -2x -3 = 0
(x-3)(x+1)=0
x=3 or x=-1
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Cheers,
Stan H.