Question

How do you simplify `(3x)/4-(5x)/6`?

Answer 1

`(3x)/4-(5x)/6=-x/12`

Explanation:

`(3x)/4-(5x)/6`

`color(red)(3/3)*(3x)/4-color(blue)(*2/2)(5x)/6`

`(9x)/12-(10x)/12`

`(9x-10x)/12`

`-x/12`

Answer 2

`-x/12`

Explanation:

Before subtracting the fractions we require them to have a `color(blue)"common denominator"`

Multiplying the numerator/denominator of `(3x)/4` by 6 and

`(5x)/6` by 4 will ensure this.

`((3x)/4xx6/6)-((5x)/6xx4/4)`

`=(18x)/24-(20x)/24`

Now there is a common denominator we can subtract the numerators leaving the denominator as it is.

`=(-2x)/24=-(cancel(2)^1 x)/cancel(24)^12=-x/12`