How do you solve #x/(x-5) - 2/(x+5) = 50/(x^2-25)#?
Start by multiplying both sides by the Least Common Denominator.
The Least Common Denominator is
Above we have multiplied all numerators by the LCD and canceled out terms with the denominator where needed.
Now distribute and add like terms.
Note that we need to solve for 0 in order to solve by factoring.
Factor the left side:
Solve each factor for 0:
HOWEVER the second answer must be eliminated since it would result in a zero denominator (extraneous solution).
So the only valid answer is
Hope this helps!