Question 54462
24/x-3 = 72/x+3 [Find the LCD= (x-3)(x+3)]
.
(x-3)(x+3)(24/x-3) = (x-3)(x+3)(72/x+30) [Multiply each fraction by the LCD]
.
(x+3)(24) = (x-3)(72) [Cancel wherever possible]
.
(24x+72) = (72x-216)  [Simplify]
.
24x+72-72x+216=0  [Set the equation equal to zero]
.
-48x+288=0  [Combine like-terms]
.
-48x+288-288=0-288=0 [Solve for x]
-48x=-288
x=-288/-48
6

.
Check by plugging (x=6) back into the original equation.