Question

How do you solve `2/(3x) + 5 = 4/x`?

Answer 1

`x=2/3`

Explanation:

Solve:

`2/(3x)+5=4/x`

Multiply both sides by `3x`.

`3x(2/(3x)+5)=(4xx3x)/x`

Cancel.

`color(red)cancel(color(black)(3x))(2/(color(red)cancel(color(black)(3x))))+5xx3x=(4/color(red)cancel(color(black)(x)))3color(red)cancel(color(black)(x))`

Simplify.

`2+5xx3x=4xx3`

`2+15x=12`

Subtract `2` from both sides.

`2-2+15x=12-2`

Simplify.

`0+15x=10`

`15x=10`

Divide both sides by `15`.

`(color(red)cancel(color(black)(15))^1x)/color(red)cancel(color(black)(15))^1=10/15`

`x=10/15`

Reduce by dividing the numerator and denominator by `5`.

`x=(10-:5)/(15-:5)`

`x=2/3`