Question

Perform the operation and combine to one fraction.
start fraction, 1, divided by, x, squared, minus, 8, x, plus, 12, end fraction, minus, start fraction, 2, divided by, x, minus, 2, end fraction
x
2
−8x+12
1
​
−
x−2
2

Answer 1

Factor the quadratic: x^2 − 8x + 12 = (x − 2)(x − 6).

Rewrite with common denominator (x − 2)(x − 6):
1/((x−2)(x−6)) − 2/(x−2) = 1/((x−2)(x−6)) − 2(x−6)/((x−2)(x−6))

Combine numerators:
= (1 − 2(x − 6))/((x − 2)(x − 6)) = (1 − 2x + 12)/((x − 2)(x − 6))

Simplify numerator:
= (13 − 2x)/((x − 2)(x − 6))

Domain: x ≠ 2, 6.