Perform the following operation and express in simplest form.

Question

start fraction, x, squared, minus, 64, divided by, x, squared, minus, 9, x, end fraction, dot, start fraction, x, plus, 9, divided by, x, squared, plus, x, minus, 72, end fraction
x
2
−9x
x
2
−64
​
⋅
x
2
+x−72
x+9
​

Answer 1

To simplify, we can factor the numerator and denominator separately.

Numerator:
x^2 - 64 can be factored as (x + 8)(x - 8).

Denominator:
x^2 - 9x can be factored as x(x - 9).

The expression becomes:
((x + 8)(x - 8))/(x(x - 9)) * (x + 9)/(x^2 + x - 72)

Next, we can cancel out common factors:
(x + 8)(x - 8)/(x(x - 9)) * (x + 9)/((x - 8)(x + 9))

The (x + 8) terms and (x + 9) terms cancel out:
1/(x(x - 9))

Therefore, the expression simplifies to 1/(x(x - 9)).