SOLUTION: equations involving rational expressions. solve and check each of the following equations for x. x / x - 2 - x + 1 / x = 8 / x ^ 2 - 2 x so far i have... x / x

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Question 73730: equations involving rational expressions.
solve and check each of the following equations for x.
x / x - 2 - x + 1 / x = 8 / x ^ 2 - 2 x
so far i have...
x / x - 2 - x + 1 / x = 8 / x ( x - 2 )
x ( x - 2 )* x / x - 2 - x ( x - 1 ) * x + 1 / x = x ( x - 2 ) * 8 / x ( x - 2 )
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Your problem statement was a little confusing. It would have helped if you had used some
more parentheses to separate the quantities. But because you provided your work I think I
was able to sort things out after seeing what you were doing.
.
I think that the problem you are working on is to find a solution to this equation:
.

.
You saw that the critical beginning was to factor the denominator on the right side. Good
for you. Factoring that denominator results in:
.

.
After this point, I had a little difficulty seeing what you had done, so let me just proceed
from this point without commenting on your work. The next step is to put all the terms in
this equation over a common denominator so you can combine them. As it turns out, the
common denominator is which is the denominator of the right side.
.
To put the first term on the left side over the common denominator you need to multiply it
by and to put the second term on the left side over the common denominator
you need to multiply it by . When you do those multiplications you get:
.

.
Now if you multiply all three terms in this equation by the common denominator
then that multiplier appears in the numerator of all three terms and it cancels with the
common denominator.
The result is that the problem is reduced to:
.

.
[Another way of looking at this is that since all the fractions in the equation had the same
denominator, then the numerators must combine to be equal.]
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Anyhow, the first term on the left side is and the second term multiplies out
(using the FOIL method, or whatever method you are familiar with) to and
the equation becomes:
.

.
Remove the parentheses by changing the signs of all the terms within them to make the equation:
.

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The first two terms and cancel each other out and you are left with:
.

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Eliminate the +2 from the left side by adding -2 to both sides and you finally end up with:
.

.
That's the answer. I hope you could follow the above and that it helps you to find whether
you were on the right track to get a solution too.
.

SOLUTION: equations involving rational expressions. solve and check each of the following equations for x. x / x - 2 - x + 1 / x = 8 / x ^ 2 - 2 x so far i have... x / x - 2 -