Question

How do you solve `3/(2y-7) = 3/y`?

Answer 1

Clear the fractions and solve a 2-step equation to get a solution of `y=7`.

Explanation:

We first want to clear the fraction on the left side of the equation. We do that by multiplying by `2y-7`:
`3/(2y-7)=3/y`

`->3/(2y-7)(2y-7)=3/y(2y-7)`

`->3/cancel((2y-7))cancel((2y-7))=3/y(2y-7)`

`->3=(3(2y-7))/y`

Now we clear the `y` from the right, by multiplying by `y`:
`3=(3(2y-7))/y`

`->3*y=(3(2y-7))/y*y`

`->3*y=(3(2y-7))/cancel(y)*cancel(y)`

`->3y=3(2y-7)`

Distributing the `3` on the right gives us:
`3y=3(2y-7)`
`->3y=6y-21`

Now we just have to solve this two-step equation, and we have `y`:
`3y=6y-21`

`->-3y=-21`

`->y=(-21)/-3=7`