Question

How do you solve `\frac { 1} { 3} - \frac { x - 2} { 2x + 4} = \frac { 2+ x } { 3x + 6}`?

Answer 1

`x=2`

Explanation:

We can rewrite the fraction as (take out a `2` and `3` from the denominators of the second and third fractions, repectively):

`\frac { 1} { 3} - \frac { (x - 2)/2} { x + 2} = \frac { (2+ x)/3 } { x + 2}`

On the right side, the fraction simplifies to just `1/3`. Thus,

`\frac { 1} { 3} - \frac { (x - 2)/2} { x + 2} = \frac { 1} { 3}`

So
`0=\frac { (x - 2)/2} { x + 2}`

Multiply both sides by the denominator,

`(x-2)/2=0`

`x-2=0`

and

`x=2`.

We plug in `x` to the orginial equation, and since it is not extraneous, it is a solution to the equation.