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

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

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Answer 1 · 2018-03-12T04:37:48

$v = - 6 .$ $v=-6.$

Explanation:

$\frac{v - 6}{v - 4} = \frac{v}{v + 1}$ $(v-6)/(v-4)=v/(v+1)$

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

or, $v^{2} - 5 v - 6 = v^{2} - 4 v$ $v^2-5v-6=v^2-4v$

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

Simplifying further,

$- v - 6 = 0$ $-v-6=0$

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

Plugging in the value of $v$ $v$ in the equation,
Left hand side is:
$\frac{v - 6}{v - 4} = \frac{- 6 - 6}{- 6 - 4} = \frac{- 12}{- 10} = \frac{6}{5}$ $(v-6)/(v-4)=(-6-6)/(-6-4)=(-12)/-10=6/5$

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

$\frac{v}{v + 1} = - \frac{6}{- 6 + 1} = \frac{- 6}{- 5} = \frac{6}{5}$ $v/(v+1)=-6/(-6+1)=(-6)/-5=6/5$

Thus, $L H S = R H S$ $LHS=RHS$ in the equation.

Hope this helps!!

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

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