SOLUTION: x/x-1 + 2/x-5=-4/(x-1)(x-5) solve the eqution for x

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Question 5069: x/x-1 + 2/x-5=-4/(x-1)(x-5) solve the eqution for x







Answer by guapa(62) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-1%29%2B2%2F%28x-5%29=-4%2F%28x-1%29%28x-5%29
First of all we have to make a restriction to avoid division by 0. x can not be 1 or 5. (x-1)=1-1=0, (x-5)=5-5=0
Now you have to find the LCD which is (x-1)(x-5). Now find equivalent fractions with a common denominator. The advantage here is that by using the LCD you clear the equation of all fractions.

x%28x-5%29%2B2%28x-1%29=-4 Use the distributive property to get rid of the parentheses.
x%5E2-5x%2B2x-2=-4 add 4 to both sides and combine like terms.
x%5E2-3x%2B2=0 Change the middle term into 2 numbers whose sum is -3 and whose product is 2. (-2,-1) -2+(-1)=-3, -2(-1)=2
x%5E2-2x-x%2B2=0 Factor by grouping
x%28x-2%29-1%28x-2%29=0 Combine like terms
%28x-1%29%28x-2%29=0
Solve for x
a)x-1=0, x=1
b)x-2=0, x=2
Since we made a restriction you can see that solution a) cannot be correct.
So, (2) is the solution set.
Check it:
2%2F%282-1%29%2B2%2F%282-5%29=-4%2F%282-1%29%282-5%29
2%2F1%2B2%2F-3=-4%2F-3
2%2F1-2%2F3=4%2F3 Use the LCD (3)
6-2=4
4=4
Hope it helps