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

1 Answer
Candy
Mar 12, 2018

v=-6.v=−6.

Explanation:

(v-6)/(v-4)=v/(v+1)v−6v−4=vv+1

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

or, v^2-5v-6=v^2-4vv2−5v−6=v2−4v

Cancelling the v^2v2 on both sides,
we have:
-5v-6=-4v−5v−6=−4v

Simplifying further,

-v-6=0−v−6=0

or, -v=6−v=6
Thus, we have, v=-6v=−6

Plugging in the value of vv in the equation,
Left hand side is:
(v-6)/(v-4)=(-6-6)/(-6-4)=(-12)/-10=6/5v−6v−4=−6−6−6−4=−12−10=65

Plugging in the value of vv in the Right hand side:

v/(v+1)=-6/(-6+1)=(-6)/-5=6/5vv+1=−6−6+1=−6−5=65

Thus, LHS=RHSLHS=RHS in the equation.

Hope this helps!!

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