Question 347966
{{{(z-1)/(z-8) - (z+1)/(z+8) + (z-120)/(z^2-64)}}} Start with the given expression.



{{{(z-1)/(z-8) - (z+1)/(z+8) + (z-120)/((z-8)(z+8))}}} Factor the last denominator.



{{{((z-1)(z+8))/((z-8)(z+8)) - (z+1)/(z+8) + (z-120)/((z-8)(z+8))}}} Multiply the first fraction by {{{(z+8)/(z+8)}}}



{{{((z-1)(z+8))/((z-8)(z+8)) - ((z+1)(z-8))/((z-8)(z+8)) + (z-120)/((z-8)(z+8))}}} Multiply the second fraction by {{{(z-8)/(z-8)}}}



{{{(z^2+7z-8)/(z^2-64) - (z^2-7z-8)/(z^2-64) + (z-120)/(z^2-64)}}} FOIL



{{{(z^2+7z-8- (z^2-7z-8)+z-120)/(z^2-64)}}} Combine the fractions.



{{{(z^2+7z-8- z^2+7z+8+z-120)/(z^2-64)}}} Distribute.



{{{(15z-120)/(z^2-64)}}} Combine like terms.



{{{(15(z-8))/(z^2-64)}}} Factor the numerator.



{{{(15(z-8))/((z-8)(z+8))}}} Factor the numerator.



{{{(15*cross((z-8)))/(cross((z-8))(z+8))}}} Cancel out the common terms.



{{{15/(z+8)}}} Simplify.



So {{{(z-1)/(z-8) - (z+1)/(z+8) + (z-120)/(z^2-64)=15/(z+8)}}}



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