SOLUTION: 1/x+1+5x/x-2=3

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Question 1066295: 1/x+1+5x/x-2=3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
What you meant is
1/(x+1)+5x/(x-2)=3 ,
because
1/(x+1)+5x/(x-2) means 1%2F%28x%2B1%29%2B5x%2F%28x-2%29 ,
but 1/x+1+5x/x-2 means 1%2Fx%2B1%2B5x%2Fx-2 .

From 1%2F%28x%2B1%29%2B5x%2F%28x-2%29=3 ,
we can start by multiplying both sides of the equal sign times %28x%2B1%29%2A%28x-2%29 to get
,
which simplifies to
x-2%2B5x%2A%28x%2B1%29=3%2A%28x%5E2-x-2%29 ,
x-2%2B5x%5E2%2B5x=3x%5E2-3x-6 .
Adding -3x%5E2%2B3x%2B6 to both sides of the equal sign, we get the equivalent equation
2x%5E2%2B9x%2B4=0 ,
which we could factor to get
%282x%2B1%29%28x%2B4%29=0 ,
to find that
either 2x%2B1=0 ---> highlight%28x=-1%2F2%29 ,
or x%2B4=0 ---> highlight%28x=-4%29 .