Question 344657
Perform the indicated operations and simplify

x-3/x-4 - x-1/x+4 + x-12/x^2-16


{{{(x - 3)/(x - 4) - (x - 1)/(x + 4) + (x - 12)/(x^2 - 16)}}}


{{{((x - 3)(x + 4) - (x - 1)(x - 4) + (x - 12))/((x - 4)(x + 4))}}} ---- Multiplying expression by LCD, (x - 4)(x + 4)


{{{(x^2 + x - 12 - (x^2 - 5x + 4) + x - 12)/((x - 4)(x + 4))}}} ------ Expanding numerator of expression


{{{(x^2 + x - 12 - x^2 + 5x - 4 + x - 12)/((x - 4)(x + 4))}}}


{{{(x^2 - x^2 + x + 5x + x - 12 - 4 - 12)/((x - 4)(x + 4))}}} ------ Collecting like-terms in numerator


{{{(7x - 28)/((x - 4)(x + 4))}}} ------ Combining like-terms in numerator


{{{(7(x - 4))/((x - 4)(x + 4))}}} ------ Factoring numerator


{{{(7cross((x - 4)))/(cross((x - 4))(x + 4))}}} ------ Canceling like-terms in numerator and denominator


{{{highlight_green(7/(x + 4))}}}