Simplify the rational expression. State any restrictions on the variables. 𝑥 2−5𝑥−24 𝑥 2−7𝑥−30 a. 𝑥−8 𝑥−10 ; 𝑥 ≠ 3 𝑜𝑟 − 10 b. 𝑥+8 𝑥+10 ; 𝑥 ≠− 10 c. 𝑥−8 𝑥−10 ; 𝑥 ≠− 3 𝑜𝑟 10 d. 𝑥+8 𝑥+10 ; 𝑥 ≠ 3 𝑜𝑟 − 10

Question

Simplify the rational expression. State any restrictions on the variables. 𝑥 2−5𝑥−24 𝑥 2−7𝑥−30 a. 𝑥−8 𝑥−10 ; 𝑥 ≠ 3 𝑜𝑟 − 10 b. 𝑥+8 𝑥+10 ; 𝑥 ≠− 10 c. 𝑥−8 𝑥−10 ; 𝑥 ≠− 3 𝑜𝑟 10 d. 𝑥+8 𝑥+10 ; 𝑥 ≠ 3 𝑜𝑟 − 10

Answer 1

To simplify the rational expression, first factor both the numerator and the denominator:

Numerator: x^2 - 5x - 24 = (x - 8)(x + 3)
Denominator: x^2 - 7x - 30 = (x - 10)(x + 3)

Now divide out any common factors:
(x - 8)/(x - 10)

The simplified rational expression is: (x - 8)/(x - 10)

The restriction on the variable is x cannot equal 10.