SOLUTION: What are the steps to solving this problem? (2/(x-1))-(5/x)=(10/(x^2-x))

Question 220103: What are the steps to solving this problem? (2/(x-1))-(5/x)=(10/(x^2-x))
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
What are the steps to solving this problem? (2/(x-1))-(5/x)=(10/(x^2-x))
Step 1: Observe that on the right side, the denominator, (x^2-x) can be factored to x(x-1), so let's do that and re-write the equation. Now we have:
2/(x-1)-(5/x)=10/x(x-1)
Step 2: Observe that if we multiply each term in the equation by x(x-1), we completely rid ourselves of the fractions. Now let's do that:
(2x(x-1))/(x-1) -(5x(x-1))/x =10x(x-1)/x(x-1) simplify by cancelling and we get:
2x-5(x-1)=10
Step3: we simplify the above equation by getting rid of parens and collecting like terms and we get
2x-5x+5=10 subtract 5 from each side
2x-5x+5-5=10-5 collect like terms
-3x=5 divide each side by -3
x=-(5/3)----------answer
CK
Substitute x=-(5/3) in the original equation:
(2/((-5/3)-1))-(5/(-5/3)=(10/((-5/3)^2-(-5/3))
2/(-8/3)-(-3)=10/(25/9+15/9)
(-6/8)+(24/8)=9/4
18/8=9/4
9/4=9/4
Hope this helps---ptaylor
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