Question

Explanation & answer

Answer 1

The answer to this expression is
`(13x-6)/(6)`, or
`(13x)/(6) - 1`.

Explanation:

The given problem is
`\displaystyle (2x)/(3)+((3)x-2)/(2)` .

Let's start by finding common denominators for the fractions so that we can add them. The simplest common denominator is 6; we multiply
`(2x)/(3)` by
`(2)/(2)` and
`(3x-2)/(2)` by
`(3)/(3)`.

• 
  `\displaystyle (2x)/(3) * (2)/(2) =(4x)/(6)`
• 
  `\displaystyle (3x-2)/(2) * (3)/(3) = (3(3x-2))/(6) = (9x-6)/(6)`

Now, since the fractions have common denominators, we can add them together.

• 
  `\displaystyle (4x)/(6) + (9x-6)/(6) = (13x-6)/(6)`

The answer to this expression is
`(13x-6)/(6)`, or
`(13x)/(6) - 1`.