find the difference. express your answer in simplest form.
x^2 + 3 / x - 2x^2 + 5 / x
a)-x^2 - 8 / 2x
b)-x^2 - 2 / x
c)3x^2 - 8 / 2x
d) 3x^2 - 8 /x
X^2 +3/X- 2X^2 +5/X. Common Denominator
=X: (X^3+3)/X -(2X^3+5)/X=
(X^3+3)/X+(-2X^3-5)/X=(-X^3-2)/X=
-X^3/X-2/X=-X^2-2/X
To find the difference, we need to subtract the second fraction from the first fraction.
The first fraction is (x^2 + 3) / (x), and the second fraction is (5 - 2x^2) / (x).
To subtract these fractions, we need to find a common denominator. In this case, the common denominator is 'x'.
So, the two fractions can be rewritten with the common denominator:
(x^2 + 3) / (x) - (5 - 2x^2) / (x)
Now, we can combine the numerators:
[(x^2 + 3) - (5 - 2x^2)] / (x)
Simplifying the numerators:
(x^2 + 3 - 5 + 2x^2) / (x)
Combine like terms:
(3x^2 - 2) / (x)
Therefore, the difference is (3x^2 - 2) / (x).
In the given answer choices:
a) -x^2 - 8 / 2x
b) -x^2 - 2 / x
c) 3x^2 - 8 / 2x
d) 3x^2 - 8 / x
None of the given answer choices match the simplified form of (3x^2 - 2) / (x).
The correct simplified form is (3x^2 - 2) / (x).