SOLUTION: Please help me solve this equation: x/x-8 + 6/x-4= x^2/x^2-12x+32

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Question 198863This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation:
x/x-8 + 6/x-4= x^2/x^2-12x+32 This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%29%2F%28x-8%29%2B%286%29%2F%28x-4%29=%28x%5E2%29%2F%28x%5E2-12x%2B32%29 Start with the given equation.


%28x%29%2F%28x-8%29%2B%286%29%2F%28x-4%29=%28x%5E2%29%2F%28%28x-8%29%28x-4%29%29 Factor the last denominator.


Multiply every term on both sides by the LCD %28x-8%29%28x-4%29. Doing this will eliminate all of the fractions.


x%28x-4%29%2B6%28x-8%29=x%5E2 Simplify


x%5E2-4x%2B6x-48=x%5E2 Distribute


x%5E2-4x%2B6x-48-x%5E2=0 Subtract x%5E2 from both sides.


2x-48=0 Combine like terms.


2x=0%2B48 Add 48 to both sides.


2x=48 Combine like terms on the right side.


x=%2848%29%2F%282%29 Divide both sides by 2 to isolate x.


x=24 Reduce.


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Answer:

So the solution is x=24