Question

How do you multiply `3 /(x - 1) + 1 / (x(x - 1)) = 2 / x`?

Answer 1

Assuming the question really was "solve for "`x`:
`color(white)("XXX")x=-3`

Explanation:

1 Multiply both sides by the Least Common Denominator [namely `x(x-1)`]
`color(white)("XXX")3x+1=2(x-1)`

2 Simplify
`color(white)("XXX")3x+1=2x-2`

3 Subtract `2x` from both sides
`color(white)("XXX")3x+1-2x=-2`

4 Simplify `3x+1-2x` to `x+1`
`color(white)("XXX")x+1=-2`

5 Subtract `1` from both sides
`color(white)("XXX")x=-2-1`

6 Simplify
`color(white)("XXX")x=-3`

Answer 2

`x=-3`

Explanation:

Multiply the first fraction by `x`

`[3x+1]/[x(x-1)]=2/x`

Now multiply both sides by `x(x-1)` to remove the fractions

`3x+1=2(x-1)`

`3x+1=2x-2`

subtract `2x` from both sides

`x+1=-2`

subtract 1 from both sides