which shows the expression $\frac{x^{2}-1}{x^{2}-x}$ in simplest form?\n$\frac{1}{x}$\n$\frac{x +…
which shows the expression $\frac{x^{2}-1}{x^{2}-x}$ in simplest form?\n$\frac{1}{x}$\n$\frac{x + 1}{x}$\n$\frac{x - 1}{x}$\n$\frac{1}{x + 1}$
Answer
Answer:
B. $\frac{x + 1}{x}$
Explanation:
Step1: Factor the numerator
$x^{2}-1=(x + 1)(x - 1)$
Step2: Factor the denominator
$x^{2}-x=x(x - 1)$
Step3: Simplify the fraction
$\frac{x^{2}-1}{x^{2}-x}=\frac{(x + 1)(x - 1)}{x(x - 1)}=\frac{x + 1}{x}$ (assuming $x\neq1$ and $x\neq0$)