Simplify the expression completely if possible.

Question

start fraction, 3, x, cubed, minus, 6, x, squared, divided by, x, squared, plus, x, minus, 6, end fraction
x
2
+x−6
3x
3
−6x
2

​

Answer 1

To simplify the expression completely, we can first factor the numerator and the denominator:

Numerator:
3x^3 - 6x^2

Factoring out an x^2, we get:
x^2(3x - 6)

Simplifying the expression inside the parentheses, we have:
3x - 6 = 3(x - 2)

Therefore, the numerator can be written as:
x^2 * 3(x - 2) = 3x^2(x - 2)

Denominator:
x^2 + x - 6

Factoring the quadratic, we have:
(x + 3)(x - 2)

Now we can rewrite the expression:
(3x^2(x - 2))/((x + 3)(x - 2))

We can cancel out the common factors in the numerator and denominator:
(3x^2)/((x + 3))

Therefore, the simplified expression is:
(3x^2)/(x + 3)