Question 78168
{{{(2x^-2x)/(x^2-2x-15)  -  2/(x+3)   +x/(5-x)}}}


{{{(2x^-2x)/((x-5)(x+3))  -  2/(x+3)   +x/(5-x)}}} Factor the denominator


{{{(2x^-2x)/((x-5)(x+3))  -  2/(x+3)   -x/(x-5)}}} Negate the last term to get a denominator of x-5


{{{(2x^-2x)/((x-5)(x+3))  - ((x-5)/(x-5))(2/(x+3))   -((x+3)/(x+3))(x/(x-5))}}} Multiply the 2nd term by {{{(x-5)/(x-5)}}} and the 3rd term by {{{(x+3)/(x+3)}}} to get the LCD


{{{(2x^-2x)/((x-5)(x+3))  - 2(x-5)/((x+3)(x-5))  -x(x+3)/((x+3)(x-5))}}}  Multiply

 


{{{(2x^-2x)/((x-5)(x+3))  - (2x-10)/((x+3)(x-5))  -(x^2+3x)/((x+3)(x-5))}}} Distribute


{{{(2x^-2x-2x+10-x^2-3x)/((x-5)(x+3))}}} Combine the fractions



{{{(2x^-2x-5x+10-x^2)/((x-5)(x+3))}}} Combine like terms. This is your simplified form.