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

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

Answer by guapa(62) (Show Source): You can put this solution on YOUR website!

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.

Use the distributive property to get rid of the parentheses.
add 4 to both sides and combine like terms.
Change the middle term into 2 numbers whose sum is -3 and whose product is 2. (-2,-1) -2+(-1)=-3, -2(-1)=2
Factor by grouping
Combine like terms

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:

Use the LCD (3)

Hope it helps

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