Question

divide and state the quotient in simplest form. (\frac{x^{2}-9x + 18}{x^{2}+x - 12}div\frac{x^{2}+x - 12}{x + 1}) (\frac{x - 6}{x + 4}) (\frac{x + 4}{x - 6}) (\frac{x^{2}-9x + 18}{x^{2}+x - 12}) (\frac{x^{2}+x - 12}{x^{2}-9x + 18}) (\frac{-3}{2})

Explanation:

Step1: Perform polynomial long - division

We divide \(x^{2}-9x + 18\) by \(x^{2}+x - 12\). First, factor the polynomials. \(x^{2}-9x + 18=(x - 3)(x - 6)\) and \(x^{2}+x - 12=(x + 4)(x-3)\).

Step2: Simplify the rational expression

\(\frac{x^{2}-9x + 18}{x^{2}+x - 12}=\frac{(x - 3)(x - 6)}{(x + 4)(x - 3)}\). Cancel out the common factor \((x - 3)\) (assuming \(x
eq3\)).

Answer:

\(\frac{x - 6}{x + 4}\)