SOLUTION: Solve the equation: (7/(2x+1))-(8x/(2x-1))=-4 I'm really bad at the equations with fractions! :)

Question 95951This question is from textbook Precalculus with limits
: Solve the equation: (7/(2x+1))-(8x/(2x-1))=-4
I'm really bad at the equations with fractions! :) This question is from textbook Precalculus with limits

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given to solve:
.

.
If you don't like fractions, in this case you can get rid of the fractions. How? Begin by noting
that is a common denominator. Suppose that we multiply both sides of this
equation (all terms) by . In doing that multiplication you make the original
problem become:
.

.
Next, where it applies you can cancel the denominator with the like term in the numerator as
follows:
.

.
After these cancellations you are left with:
.

.
Multiplying results in
.
Multiplying results in
.
and finally,
.
Multiplying results in
.
Substitute these results into the equation and you have:
.

.
On the left side you can remove the parentheses if you change the signs of the terms inside
the parentheses to get:
.

.
Notice that you have on both sides. Therefore, if you add to
both sides these two terms disappear and you are left with:
.

.
On the left side you can combine the and the to get to reduce
the equation to:
.

.
Then get rid of the -7 on the left side by adding 7 to both sides to get:
.

.
Finally, solve for x by dividing both sides by 6 to get:
.

.
This is the answer you are looking for ...
.
You can check this answer by substituting for x in the original problem and
ensuring that the equation will balance.
.
Hope this helps you to understand the problem and how you can get rid of the denominators in
the equation so that you are not working with fractions.
.

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