question\nperform the operation and combine to one fraction.\n$\frac{1}{x - 1}-\frac{5}{x}$

Explanation:

Step1: Find common denominator

The common denominator of $x - 1$ and $x$ is $x(x - 1)$. So we rewrite the fractions: $\frac{1}{x - 1}\times\frac{x}{x}-\frac{5}{x}\times\frac{x - 1}{x - 1}=\frac{x}{x(x - 1)}-\frac{5(x - 1)}{x(x - 1)}$.

Step2: Subtract the numerators

$\frac{x-5(x - 1)}{x(x - 1)}=\frac{x-5x + 5}{x(x - 1)}$.

Step3: Simplify the numerator

$\frac{x-5x + 5}{x(x - 1)}=\frac{-4x + 5}{x(x - 1)}$.

Answer:

$\frac{-4x + 5}{x(x - 1)}$