Question

How do you add `\frac { 5x + 4} { 2x } + \frac { 2x + 1} { 3x }`?

Answer 1

See the entire solution process below:

Explanation:

To add fractions the two fractions need to be over common denominators. In this case, we can use a common denominator of `6x`. To get each fraction over the common denominator of `6x` we must multiply each fraction by the appropriate form of `1`:

`(3/3 xx (5x + 4)/(2x)) + (2/2 xx (2x + 1)/(3x))`

`((3(5x + 4))/(3 xx 2x)) + ((2(2x + 1))/(2 xx 3x))`

`((3xx5x) + (3xx4))/(6x) + ((2xx2x) + (2xx1))/(6x)`

`(15x+12)/(6x) + (4x+2)/(6x)`

We can next add the numerators of the two fractions:

`(15x+12 + 4x+2)/(6x)`

We can now group and combine like terms in the numerator:

`(15x + 4x +12+2)/(6x)`

`(19x +14)/(6x)`