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

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) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Factor to get

Multiply every term by the LCD to clear out the fractions.

Distribute.

Get every term to the left side.

Rearrange the terms.

Multiply every term by -1 to make the leading coefficient positive.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the solutions are or
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