Question

Simplify the following rational expression:**

6x^3 - 10x^2/3x^3 - 2x^2 - 5x})

a) (2x^2 - 5x)
b) (2x^2 + 5x)
c) (2x^2 - 7x)
d) (2x^2 + 7x)

Answer 1

To simplify the rational expression 6x^3 - 10x^2 / 3x^3 - 2x^2 - 5x, factor out the greatest common factor, which is 2x^2. Then, simplify by cancelling out the common factor.

Step-by-step explanation:

To simplify the rational expression 6x^3 - 10x^2 / 3x^3 - 2x^2 - 5x, we can start by factoring out the greatest common factor from both the numerator and the denominator. The greatest common factor in this case is 2x^2. So, we can rewrite the expression as:

(2x^2)(3x - 5) / (2x^2)(3x - 2 - 5/x)

Cancelling out the common factor, we get:

(3x - 5) / (3x - 2 - 5/x)

Therefore, the simplified rational expression is (3x - 5) / (3x - 2 - 5/x).