Question

How do you solve `v/(v-9)=10/6`?

Answer 1

`v = 22.5`
Get rid of the denominators by multiplying both sides by `color(red)(6 (v -9))` Then solve for `v`

Explanation:

By multiplying both sides by the LCD of both denominators, the denominators are eliminated and the problem is simplified.

`color(red)(6( v-9))xx v/(v-9) = color(red)(6( v-9)) xx 10 / 6`

Because `((v-9))/(( v-9)) = 1 and 6/6 = 1` this allows us to cancel.

`color(red)(6cancel(( v-9)))xx v/cancel(v-9) = color(red)(cancel6( v-9)) xx 10/cancel6`

This leaves the equation as

`6 ( v )` = `(v-9) xx 10`

Multiplying across the parenthesis gives

`6v = 10 v - 90`

Subtract `10v` from both sides. (Remember when you're trying to solve or find something always work backwards. PE SAD M -4

Do Parathesis and exponent first then do subtraction and addition from left to right, before doing division and multiplication from left to right.

`6v - 10v = 10v - 10v - 90`

this leaves

`-4v = - 90`

Now divide both sides by `-4` to solve for `v`

`(-4 v)/-4 = (-90)/(-4)`

this gives

`v = + 22.5`