SOLUTION: (7/(2x+1))-(8x/(2x-1))=-4

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Question 701553: (7/(2x+1))-(8x/(2x-1))=-4
Answer by Simnepi(216) About Me  (Show Source):
You can put this solution on YOUR website!
First thing in problems like this is to get rid of those horrible fractions!
%287%2F%282x%2B1%29%29-%288x%2F%282x-1%29%29=-4
If we multiply each term through the equation by (2x+1) we get
%282x%2B1%29%287%2F%282x%2B1%29%29-%282x%2B1%29%288x%2F%282x-1%29%29=%282x%2B1%29%28-4%29 the 2x+1 in the denominator of the first term will cancel with the 2x+1 on the top line
giving 7-%282x%2B1%29%288x%2F%282x-1%29%29=%282x%2B1%29%28-4%29
that's got rid of the fraction from the first term so lets do a similar thing to the get rid of the second fraction.
This time we'll multiply each term by 2x-1 this will cancel with the denominator in the second fraction to give
%282x-1%29%287%29-%282x%2B1%29%288x%29=%282x%2B1%29%282x-1%29%28-4%29
Now we can multiply out all those brackets gives
14x-7-16x%5E2-8x=-16x%5E2%2B4
Simplifying gives
6x=3 therefore dividing by 6 gives
x=1%2F2