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

2 Answers
Oct 17, 2017

(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)

Oct 17, 2017

(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)