Perform the following operation and express in simplest form.

Question

start fraction, x, cubed, divided by, x, squared, minus, 4, end fraction, divided by, start fraction, 2, x, divided by, x, squared, minus, 7, x, plus, 10, end fraction
x
2
−4
x
3

​
÷
x
2
−7x+10
2x
​

Answer 1

To simplify this expression, we need to combine the fractions and simplify the resulting fraction.

Start by simplifying the numerator (x^3).

Next, we can simplify the denominator (x^2 - 4) by factoring it as (x + 2)(x - 2).

Start fraction, x^3, divided by, (x + 2)(x - 2), divided by, (2x)/(x^2 - 7x + 10).

Now we can cancel out common factors between the numerator of the first fraction and the denominator of the second fraction, as well as the denominator of the first fraction and the numerator of the second fraction.

(x^3)/(x + 2)(x - 2) ÷ (2x)/(x^2 - 7x + 10) = (x^3)/(2x(x^2 - 7x + 10))

Next, we can simplify the resulting fraction (x^3)/(2x(x^2 - 7x + 10)) by canceling out the common factor of x in the numerator and denominator.

(x^3)/(2x(x^2 - 7x + 10)) = (x^2)/(2(x^2 - 7x + 10))

Therefore, the simplified expression is (x^2)/(2(x^2 - 7x + 10)).