Question

select the correct answer.
which polynomial is equivalent to this expression?
\frac{(x + 2)(x - 1)}{x - 1}
a. \\ x - 1
b. \\ (x + 2)(x - 1)
c. \\ x + 1
d. \\ x + 2

Explanation:

Step1: Identify the domain

We note that for the expression \(\frac{(x + 2)(x - 1)}{x - 1}\) to be well - defined, \(x
eq1\) (because division by zero is undefined). When \(x
eq1\), we can cancel out the common factor \((x - 1)\) in the numerator and the denominator.

Step2: Simplify the expression

Using the rule of fraction simplification \(\frac{a\times b}{b}=\ a\) (where \(b
eq0\)), here \(a=(x + 2)\) and \(b=(x - 1)\) with \(x
eq1\). So \(\frac{(x + 2)(x - 1)}{x - 1}=x + 2\) (for \(x
eq1\)).

Answer:

D. \(x + 2\)