Question

How do you solve `\frac { 1} { x } + \frac { 2} { 3} = \frac { 9} { 3x }`?

Answer 1

`x = 3`

Explanation:

First, you must get the fractions on the left side of the equation to have a common denominator by multiplying each fraction by the necessary form of `1`:

`(3/3 * 1/x) + (x/x * 2/3) = 9/(3x)`

`(3 * 1)/(3 * x) + (x * 2)/(x *3) = 9/(3x)`

`3/(3x) + (2x)/(3x) = 9/(3x)`

`(3 + 2x)/(3x) = 9/(3x)`

We can now multiple each side of the equation by `3x` to eliminate the fraction and keep the equation balanced:

`3x * (3 + 2x)/(3x) = 3x * 9/(3x)`

`cancel(3x) * (3 + 2x)/cancel(3x) = cancel(3x) * 9/cancel(3x)`

`3 + 2x = 9`

Now we can solve for `x` while keeping the equation balanced:

`3 + 2x - 3 = 9 - 3`

`2x = 6`

`(2x)/2 = 6/2`

`x = 3`