Question 713404
{{{(x + 1)/(x^2 + 2x - 8) - (x)/(4x - 8)}}}


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


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


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


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


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


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


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


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


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


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


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


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


{{{-(x + 2)/(4x+16)}}}


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So 


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


simplifies to


{{{-(x + 2)/(4x+16)}}}


To avoid dividing by zero, we must make the following restrictions: {{{x<>-4}}} and {{{x<>2}}}