Question

How do you solve `(5x)/(x-1)+5=15/(x-1)`?

Answer 1

`x=color(green)(2)`

Explanation:

Given
`color(white)("XXX")(5x)/(x-1)+5 = 15/(x-1)`

Multiply both sides by `(x-1)`
`color(white)("XXX")5x+5x-5 =15`

`color(white)("XXX")rarr 10x =20`

`color(white)("XXX")rarr x=2`

Answer 2

I found: `x=2`

Explanation:

We can choose `x-1` as common denominator and write:
`(5x+5(color(red)(x-1)))/(x-1)=15/(x-1)`
Cancel the 2 denominators and rearrange:
`5x+5x-5=15`
`10x=20`
`x=20/10=2`