Simplify (2x+1)+-6/(x-1)

$(2 x + 1) + \frac{- 6}{x - 1}$

Step 1

Find the common denominator.

Write $2 x$ as a fraction with denominator $1$ .

$\frac{2 x}{1} + 1 + \frac{- 6}{x - 1}$

Multiply $\frac{2 x}{1}$ by $\frac{x - 1}{x - 1}$ .

$\frac{2 x}{1} \cdot \frac{x - 1}{x - 1} + 1 + \frac{- 6}{x - 1}$

Multiply $\frac{2 x}{1}$ by $\frac{x - 1}{x - 1}$ .

$\frac{2 x (x - 1)}{x - 1} + 1 + \frac{- 6}{x - 1}$

Write $1$ as a fraction with denominator $1$ .

$\frac{2 x (x - 1)}{x - 1} + \frac{1}{1} + \frac{- 6}{x - 1}$

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

$\frac{2 x (x - 1)}{x - 1} + \frac{1}{1} \cdot \frac{x - 1}{x - 1} + \frac{- 6}{x - 1}$

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

$\frac{2 x (x - 1)}{x - 1} + \frac{x - 1}{x - 1} + \frac{- 6}{x - 1}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 x (x - 1) + x - 1 - 6}{x - 1}$

Step 3

Simplify each term.

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot - 1 + x - 1 - 6}{x - 1}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{2 (x \cdot x) + 2 x \cdot - 1 + x - 1 - 6}{x - 1}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 2 x \cdot - 1 + x - 1 - 6}{x - 1}$

Multiply $- 1$ by $2$ .

$\frac{2 x^{2} - 2 x + x - 1 - 6}{x - 1}$

Step 4

Simplify by adding terms.

Add $- 2 x$ and $x$ .

$\frac{2 x^{2} - x - 1 - 6}{x - 1}$

Subtract $6$ from $- 1$ .

$\frac{2 x^{2} - x - 7}{x - 1}$