Answer:
Either [tex]\sf -a^2 + 3a + \dfrac{4}{a} [/tex]
Or [tex]\sf \dfrac{2a^3 + a^2 + 4}{a} [/tex]
Step-by-step explanation:
If the question is:
Find the difference of the polynomials [tex]\sf 2a^2 + 3a [/tex]and [tex]\sf 3a^2- \dfrac{4}{a}[/tex] by subtracting the second from the first
To find the difference of the polynomials [tex]\sf 2a^2 + 3a[/tex] and [tex]\sf 3a^2 - \dfrac{4}{a}[/tex], we subtract the second polynomial from the first.
[tex]\sf (2a^2 + 3a) - (3a^2 - \dfrac{4}{a}) [/tex]
Distribute the negative sign through the terms in the second polynomial:
[tex]\sf 2a^2 + 3a - 3a^2 + \dfrac{4}{a} [/tex]
Now, combine like terms:
[tex]\sf (2a^2 - 3a^2) + 3a + \dfrac{4}{a} [/tex]
Simplify the terms:
[tex]\sf -a^2 + 3a + \dfrac{4}{a} [/tex]
So, the difference of the given polynomials is [tex]\sf -a^2 + 3a + \dfrac{4}{a}[/tex].
This can be also written as:
[tex]\sf -a^2 + \dfrac{3a^2+4}{a} [/tex]
Additional comment:
If the question is:
Find the difference of the polynomials [tex]\sf 2a^2 + 3a [/tex]and [tex]\sf \dfrac{3a^2- 4}{a}[/tex] by subtracting the second from the first.
Answer:
To find the difference of the polynomials [tex]\sf 2a^2 + 3a[/tex] and [tex]\sf \dfrac{3a^2 - 4}{a}[/tex], we subtract the second polynomial from the first.
[tex]\sf (2a^2 + 3a) - \left(\dfrac{3a^2 - 4}{a}\right) [/tex]
To subtract the fractions, find a common denominator, which is [tex]\sf a[/tex]:
[tex]\sf (2a^2 + 3a) - \left(\dfrac{3a^2 - 4}{a}\right) = \dfrac{a(2a^2 + 3a)}{a} - \dfrac{3a^2 - 4}{a} [/tex]
Now, combine the fractions:
[tex]\sf \dfrac{2a^3 + 3a^2 - (3a^2 - 4)}{a} [/tex]
Simplify the terms:
[tex]\sf \dfrac{2a^3 + 3a^2 - 3a^2 + 4}{a} [/tex]
Combine like terms in the numerator:
[tex]\sf \dfrac{2a^3 + a^2 + 4}{a} [/tex]
So, the difference of the given polynomials is [tex]\sf \dfrac{2a^3 + a^2 + 4}{a}[/tex].
