Question 274521
your equation is:


{{{8x/(x+3) - 8 = (x-14)/(x-3)}}}


multiply both sides of this equation by (x+3) * (x-3) to get:


{{{(8x*(x-3)) - (8*(x-3)*(x+3)) = ((x-14)*(x+3))}}}


simplify this by removing parentheses to get:


{{{8x^2 - 24x - 8x^2 + 72 = x^2 + 3x - 14x - 42}}}


combine like terms to get:


{{{-24x + 72 = x^2 - 11x - 42}}}


add 24x and subtract 72 from both sides of this equation to get:


{{{ 0 = x^2 + 13x - 42}}}


factor this equation to get:


{{{ 0 = (x+19) * (x-6)}}}


solve for x to get:


x = -19
x = 6


plug these values into the original equation to confirm they are good.


I confirmed both values and they are both good.


your answer is x = -19 or x = 6.