Simplify (2x-1)/(x^2-x)+1/(x-1)

$\frac{2 x - 1}{x^{2} - x} + \frac{1}{x - 1}$

Factor $x$ out of $x^{2} - x$ .

Factor $x$ out of $x^{2}$ .

$\frac{2 x - 1}{x \cdot x - x} + \frac{1}{x - 1}$

Factor $x$ out of $- x$ .

$\frac{2 x - 1}{x \cdot x + x \cdot - 1} + \frac{1}{x - 1}$

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

$\frac{2 x - 1}{x (x - 1)} + \frac{1}{x - 1}$

To write $\frac{1}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2 x - 1}{x (x - 1)} + \frac{1}{x - 1} \cdot \frac{x}{x}$

Write each expression with a common denominator of $x (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x - 1}$ by $\frac{x}{x}$ .

$\frac{2 x - 1}{x (x - 1)} + \frac{x}{(x - 1) x}$

Reorder the factors of $(x - 1) x$ .

$\frac{2 x - 1}{x (x - 1)} + \frac{x}{x (x - 1)}$

Combine the numerators over the common denominator.

$\frac{2 x - 1 + x}{x (x - 1)}$

Add $2 x$ and $x$ .

$\frac{3 x - 1}{x (x - 1)}$