How do you solve #\frac { v - 6} { v - 4} = \frac { v } { v + 1}#?

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Answer 1 · 2018-03-12T04:37:48

#v=-6.#

#(v-6)/(v-4)=v/(v+1)#

or, #(v-6)(v+1)=v(v-4)#

or, #v^2-5v-6=v^2-4v#

Cancelling the #v^2# on both sides,
we have:
#-5v-6=-4v#

Simplifying further,

#-v-6=0#

or, #-v=6#
Thus, we have, #v=-6#

Plugging in the value of #v# in the equation,
Left hand side is:
#(v-6)/(v-4)=(-6-6)/(-6-4)=(-12)/-10=6/5#

Plugging in the value of #v# in the Right hand side:

#v/(v+1)=-6/(-6+1)=(-6)/-5=6/5#

Thus, #LHS=RHS# in the equation.

Hope this helps!!