Question

Perform the following operation and express in simplest form.
start fraction, x, squared, minus, 64, divided by, x, minus, 8, end fraction, divided by, start fraction, x, squared, plus, 5, x, minus, 24, divided by, 3, x, end fraction
x−8
x
2
−64
​
÷
3x
x
2
+5x−24
​

Answer 1

To solve this problem, we need to perform the operations and then simplify the expression.

The first step is to simplify the numerator:

(x^2 - 64) / (x - 8) = [(x + 8)(x - 8)] / (x - 8) = x + 8

Next, we simplify the denominator:

(x^2 + 5x - 24) / (3x) = (x + 8)(x - 3) / 3x

Now, we can divide the fractions:

(x + 8) / [(x + 8)(x - 3) / 3x] = (x + 8) * (3x) / (x + 8)(x - 3)

The (x + 8) terms cancel out, and we are left with:

3x / (x - 3)

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