How do you solve #-4+ \frac { 3} { v + 7} = \frac { 7} { ( v - 1) ( v + 7) }#?

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Answer 1 · 2018-01-24T11:03:35

#v_1=-6# and #v_2=3/4#

#-4+3/(v+7)=7/[(v-1)*(v+7)]#

#7/[(v-1)*(v+7)]-3/(v+7)=-4#

#(10-3v)/[(v-1)*(v+7)]=-4#

#10-3v=(-4)*(v-1)(v+7)#

#10-3v=(-4)*(v^2+6v-7)#

#10-3v=-4v^2-24v+28#

#4v^2+21v-18=0#

#4v^2+24v-3v-18=0#

#4v*(v+6)-3*(v+6)=0#

#(v+6)*(4v-3)=0#

Hence #v_1=-6# and #v_2=3/4#