Question 717125

{{{(x+1)/(x^2+2x-8) - (-x/(4x-8))}}}

{{{(x+1)/(x^2+2x-8) +x/4(x-2)}}}.....factor {{{x^2+2x-8}}}...replace {{{2x}}} with {{{4x-2x}}}

{{{x^2+2x-8=x^2+4x-2x-8=(x^2+4x)-(2x+8)=x(x+4)-2(x+4)=(x-2)(x+4)}}}

{{{(x+1)/((x-2)(x+4)) +x/4(x-2)}}}...LCD is {{{4(x-2)(x+4)}}}

{{{4(x+1)/(4(x-2)(x+4)) +x(x+4)/(4(x-2)(x+4))}}}


{{{(4(x+1) +x(x+4))/(4(x-2)(x+4))}}}


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


{{{(x^2+8x+4)/(4(x-2)(x+4))}}}


since denominator could not be equal to zero, restrictions on the variables are:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{domain }\left{x\,\in\,\mathbb{R}\,:\,x\,\neq\,2,\,x\,\neq\,-4\right}]