SOLUTION: Solve the following equation. (x+7)/(x^(2)-25)-(1)/(x-5)=x^(2)-4)/(x^(2)-25)

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Question 325272: Solve the following equation.
(x+7)/(x^(2)-25)-(1)/(x-5)=x^(2)-4)/(x^(2)-25)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B7%29%2F%28x%5E2-25%29-1%2F%28x-5%29=%28x%5E2-4%29%2F%28x%5E2-25%29 Start with the given equation.


Factor x%5E2-25 to get %28x%2B5%29%28x-5%29


x%2B7-1%28x%2B5%29=x%5E2-4 Multiply every term by the LCD %28x%2B5%29%28x-5%29 to clear out the fractions.


x%2B7-x-5=x%5E2-4 Distribute.


x%2B7-x-5-x%5E2%2B4=0 Get every term to the left side.


-x%5E2%2B0x%2B6=0 Rearrange the terms.


x%5E2-6=0 Multiply every term by -1 to make the leading coefficient positive.


Notice that the quadratic x%5E2-6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=0, and C=-6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Plug in A=1, B=0, and C=-6


x+=+%280+%2B-+sqrt%28+0-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--24+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-6%29 to get -24


x+=+%280+%2B-+sqrt%28+0%2B24+%29%29%2F%282%281%29%29 Rewrite sqrt%280--24%29 as sqrt%280%2B24%29


x+=+%280+%2B-+sqrt%28+24+%29%29%2F%282%281%29%29 Add 0 to 24 to get 24


x+=+%280+%2B-+sqrt%28+24+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%280+%2B-+2%2Asqrt%286%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%280%29%2F%282%29+%2B-+%282%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+0+%2B-+sqrt%286%29 Reduce.


x+=+sqrt%286%29 or x+=+-sqrt%286%29 Break up the expression.


So the solutions are x+=+sqrt%286%29 or x+=+-sqrt%286%29