Question

Determine whether the equation is an identity.

a. (𝑥+2)⁢(𝑥+1)^2=(𝑥^2+3⁢𝑥+2)⁢(𝑥+1)

b. Find (𝑓−𝑔)⁡(𝑥) for the given 𝑓⁡(𝑥) and 𝑔⁡(𝑥).

𝑓⁡(𝑥)=𝑥^2+𝑥−6;𝑔⁡(𝑥)=𝑥−2,where,𝑥≠2



(𝑓−𝑔)⁡(𝑥)=

Answer 1

a) Yes — it's an identity. Note x^2 + 3x + 2 = (x+1)(x+2), so
(x+2)(x+1)^2 = (x+2)(x+1)(x+1) = (x^2+3x+2)(x+1).

b) (f−g)(x) = f(x) − g(x) = (x^2 + x − 6) − (x − 2)
= x^2 + x − 6 − x + 2 = x^2 − 4.
Domain: x ≠ 2 (since g(x) is not defined at x = 2).