Question

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

Answer 1

`x = -2/13`

Explanation:

Step 1) Get each fraction over a common denominator, in this case `6x` by multiplying each fraction by the appropriate for of `1` in order to be able to add the fractions:

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

`(2x + 4)/(6x) + (3x - 6)/(6x) = 3`

`(2x + 4 + 3x - 6)/(6x) = 3`

`(5x - 2)/(6x) = 3`

Step 2) Multiply each side of the equation by `6x` to eliminate the fraction and keep the equation balanced:

`(6x*(5x - 2))/(6x) = 3*6x`

`5x - 2 = 18x`

Step 3) Solve for `x` using the necessary mathematics while keeping the equation balanced:

`5x - 5x - 2 = 18x - 5x`

`0 - 2 = 13x`

`-2 = 13x`

`-2/13 = (13x)/13`

`x = -2/13`