Question 333715

{{{(v^2+8v+7)/(3v^2+18v-21)}}} Start with the given expression.



{{{((v+7)(v+1))/(3v^2+18v-21)}}} Factor {{{v^2+8v+7}}} to get {{{(v+7)(v+1)}}}.



{{{((v+7)(v+1))/(3(v+7)(v-1))}}} Factor {{{3v^2+18v-21}}} to get {{{3(v+7)(v-1)}}}.



{{{(highlight((v+7))(v+1))/(3*highlight((v+7))(v-1))}}} Highlight the common terms. 



{{{(cross((v+7))(v+1))/(3*cross((v+7))(v-1))}}} Cancel out the common terms. 



{{{(v+1)/(3(v-1))}}} Simplify.



{{{(v+1)/(3v-3)}}} Distribute. 



So {{{(v^2+8v+7)/(3v^2+18v-21)}}} simplifies to {{{(v+1)/(3v-3)}}}.



In other words, {{{(v^2+8v+7)/(3v^2+18v-21)=(v+1)/(3v-3)}}}