Question

How do you solve `6/(t+2)=4/t`?

Answer 1

See the entire solution process below:

Explanation:

First, we multiple each side of the equation by t(t + 2)# to eliminate the fractions and keep the equation balanced:

`tcolor(red)(cancel(color(black)((t + 2)))) xx 6/color(red)(cancel(color(black)((t + 2)))) = color(red)(cancel(color(black)(t)))(t + 2) xx 4/color(red)(cancel(color(black)(t)))`

`t xx 6 = (t + 2) xx 4`

`6t = 4t + 8`

Next, substract `color(red)(4t)` from each side of the equation to isolate the `t` term while keeping the equation balanced:

`6t - color(red)(4t) = 4t + 8 - color(red)(4t)`

`(6 - 4)t = 4t - color(red)(4t) + 8`

`2t = 0 + 8`

`2t = 8`

Now, divide each side of the equation by `color(red)(2)` to solve for `t`:

`(2t)/color(red)(2) = 8/color(red)(2)`

`(color(red)(cancel(color(black)(2)))t)/cancel(color(red)(2)) = 4`

`t = 4`