Question

How do you simplify `\frac { 2} { x } + \frac { 5} { 3}`?

Answer 1

`(5x+6)/(3x)`

Explanation:

In order to add fractions, we want them to have a common denominator. To do this, we will multiply the first fraction by `3/3`. This is simply another form of 1, but it will enable us to obtain a common denominator when we also multiply the second fraction by `x/x`, which again is equal to 1. Since we are multiplying by forms of 1, we are not changing the problem.

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

Answer 2

`2/x+5/3=color(blue)((6+5x)/(3x)`

Explanation:

Simpllfy:

`2/x+5/3`

In order to add or subtract fractions, they must have the same denominator. Multiply the denominators to get the least common denominator (LCD):

LCD`=` `x xx3=3x`

Multiply both fractions by a fraction form of `1`, so that each fraction has the denominator `3x`. An example is `5/5=1`. Multiiplying by fraction form of `1` makes sure that the values do not change.

`2/x xxcolor(teal)3/color(teal)3+5/3xx color(magenta)x/color(magenta)x`

Simplify.

`6/(3x)+(5x)/(3x)`

Simplify.

`(6+5x)/(3x)`