How do you multiply #\frac { v + 14} { v ^ { 2} + 10v - 11} \cdot \frac { v ^ { 2} + 12v - 13} { 3v + 39}#?

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Answer 1 · 2017-03-29T11:37:25

#(v+14)/(v^2+10v-11)*(v^2+12v-13)/(3v+39)=(v+14)/(3(v+11))#

#(v+14)/(v^2+10v-11)*(v^2+12v-13)/(3v+39)#

#v^2+10v-11=(v+11)(v-1)#

#v^2+12v-13=(v+13)(v-1)#

#3v+39=3(v+13)#

#(v+14)/(v^2+10v-11)*(v^2+12v-13)/(3v+39)#

#=(v+14)/((v+11)cancel((v-1))) * (cancel((v+13))cancel((v-1)))/(3(cancel(v+13))) #

#(v+14)/(v^2+10v-11)*(v^2+12v-13)/(3v+39)=(v+14)/(3(v+11))#

Answer 2 · 2017-03-29T13:18:33

#color(red)((v+14)/(3(v+11))#

#(v+14)/(v^2+10v-11)*(v^2+12v-13)/(3v+39)#

#:.=(v+14)/((cancel(v-1)^color(red)1)(v+11))*((cancel(v-1)^color(red)1)(cancel(v+13)^color(red)1))/(3(cancel(v+13)^color(red)1))#

#:.=(v+14)/(v+11)*1/3#

#:.color(red)(=(v+14)/(3(v+11))#