Rational expression Simplify the following complex fraction

Rational expression - Simplify the following complex fraction

Rational expression - Simplify the following complex fraction x-3/x+4/2x-6/x^2-16

Solution

(x -3)/(x -4) / (2x-16)/(x^2 -16)

express x^2 -16 = (x+4)(x-4)

So, (2x-16)/(x^2 -16) = 2(x-8)/ (x+4)(x-4)

(x -3)/(x -4) / (2x-16)/(x^2 -16) = {(x-3)/(x-4)} *(x+4)(x-4)/2(x-8)

=(x -3)(x+ 4)/2(x-8) ( (x-4) gets cancelled )