SOLUTION: I am not sure how to solve this equation: 3/4=1- 3x-2/x+1

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Question 122092: I am not sure how to solve this equation:
3/4=1- 3x-2/x+1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

I'm not sure how to solve it either. It depends on whether you mean:

3%2F4=1-+3x-2%2Fx%2B1

or

3%2F4=1-+3x-2%2F%28x%2B1%29

or

3%2F4=1-+%283x-2%29%2F%28x%2B1%29

or

3%2F4=%281-+3x-2%29%2F%28x%2B1%29

I actually suspect it is the third choice, so I'll do that one. If it is
really something else, write back

3%2F4=1-+%283x-2%29%2F%28x%2B1%29

First put everything on one side.

3%2F4-1%2B+%283x-2%29%2F%28x%2B1%29=0

The next thing you need is a common denominator. Since there are no common
factors among the denominators, the product of the denominators (4%28x%2B1%29 is your LCD.

%283%28x%2B1%29-1%2A4%28x%2B1%29%2B+4%283x-2%29%29%2F4%28x%2B1%29=0

Simplify the numerator:

%283x%2B3-4x-4%2B12x-8%29%2F4%28x%2B1%29=0
%2811x-9%29%2Fx%2B1=0

Now, remember that a%2Fb=0 if and only if a=0 and b%3C%3E0

So we need to solve 11x-9=0

11x-9=0
11x=9
x=9%2F11

Check the answer

First, make sure that the solution does not cause any denominator in the
original equation to go to zero.

9%2F11%2B1%3C%3E0, so we can consider 9%2F11 as a possible solution.

3%2F4=1-+%283%289%2F11%29-2%29%2F%289%2F11%2B1%29

3%2F4=1-+%2827%2F11-22%2F11%29%2F%2820%2F11%29

3%2F4=1-+%285%2F11%29%2F%2820%2F11%29

3%2F4=1-+%285%2F11%29%2811%2F20%29

3%2F4=1-+5%2F20

3%2F4=1-+1%2F4: Answer checks.