Question 132110
{{{(v-3)/(v-8)-(v+1)/(v+8)+(v-88)/(v^2-64)}}} Start with the given expression



{{{(v-3)/(v-8)-(v+1)/(v+8)+(v-88)/((v-8)(v+8))}}} Factor {{{v^2-64}}} to get {{{(v-8)(v+8)}}}



Notice how the LCD is {{{(v-8)(v+8)}}}




{{{((v+8)/(v+8))((v-3)/(v-8))-(v+1)/(v+8)+(v-88)/((v-8)(v+8))}}} Multiply the first fraction by {{{(v+8)/(v+8)}}} to get the denominator to the LCD



{{{(v+8)(v-3)/(v-8)(v+8)-(v+1)/(v+8)+(v-88)/((v-8)(v+8))}}} Multiply the fractions


{{{(v+8)(v-3)/(v-8)(v+8)-((v-8)/(v-8))((v+1)/(v+8))+(v-88)/((v-8)(v+8))}}} Multiply the second fraction by {{{(v-8)/(v-8)}}}  to get the denominator to the LCD




{{{(v+8)(v-3)/(v-8)(v+8)-(v-8)(v+1)/(v+8)(v-8)+(v-88)/((v-8)(v+8))}}} Multiply the fractions



{{{((v+8)(v-3)-(v-8)(v+1)+(v-88))/(v-8)(v+8)}}} Combine the fractions



{{{(v^2+5*v-24-(v^2-7*v-8)+(v-88))/(v-8)(v+8)}}} Foil



{{{(v^2+5*v-24-v^2+7*v+8+v-88)/(v-8)(v+8)}}}  Distribute the negative


{{{(13*v-104)/(v-8)(v+8)}}} Combine like terms



{{{13(v-8)/(v-8)(v+8)}}} Factor out the GCF 13



{{{13cross((v-8))/cross((v-8))(v+8)}}} Cancel like terms



{{{13/(v+8)}}} Simplify







----------------------------------------------


Answer: 



So {{{(v-3)/(v-8)-(v+1)/(v+8)+(v-88)/(v^2-64)}}}  simplifies to  {{{13/(v+8)}}}


In other words, {{{(v-3)/(v-8)-(v+1)/(v+8)+(v-88)/(v^2-64)=13/(v+8)}}} where {{{v<>8}}}