Question

How do you combine `4/(3p)-5/(2p^2)`?

Answer 1

`(8p-15)/(6p^2)`

Explanation:

First get common denominators.

`3p` and `2p^2` will have the least common multiple of `6p^2`

We can find this by looking at one term, determining what factors it is missing from the other term, and then multiplying those factors in.

`3p = 3 * p`
`2p^2 = 2 * p * p`

They both have a `p`, so let's take the first one and give it the ones the second one has except for a `p`.
`3*p color(blue)( * 2 * p) = 6p^2`

Now we multiply each fraction by a unit factor to get the common denominator.

`4/(3p) - 5/(2p^2)`

`color(blue)((2p)/(2p))*4/(3p) - color(blue)(3/3)*5/(2p^2)`

`(8p)/(6p^2) - 15/(6p^2)`

Now we can finally combine the fractions

`(8p-15)/(6p^2)`

Answer 2

`(8p-15)/(6p^2)`

Explanation:

Take L CM for the denominator:

Factors of 3p are `3, color(red)p`
Factors of `2p^2` are `2, p, color(red)p`

L C M of the Denominator is `3* 2* p* color(red)p= 6p^2`
`color(red)p` is used only once as it is appearing in both.

Combining the two terms,
`(4/(3p))-(5/(2p^2)) = ((4*2*p)-(5*3))/(6p^2)`
`=(8p-15)/(6p^2)`