Simplify ((2x-1)/(x+1))÷((3x^2)/(x^2+x))

$\frac{2 x - 1}{x + 1} \div \frac{3 x^{2}}{x^{2} + x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x - 1}{x + 1} \cdot \frac{x^{2} + x}{3 x^{2}}$

Step 2

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

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

$\frac{2 x - 1}{x + 1} \cdot \frac{x \cdot x + x}{3 x^{2}}$

Raise $x$ to the power of $1$ .

$\frac{2 x - 1}{x + 1} \cdot \frac{x \cdot x + x^{1}}{3 x^{2}}$

Factor $x$ out of $x^{1}$ .

$\frac{2 x - 1}{x + 1} \cdot \frac{x \cdot x + x \cdot 1}{3 x^{2}}$

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

$\frac{2 x - 1}{x + 1} \cdot \frac{x (x + 1)}{3 x^{2}}$

Step 3

Cancel the common factor of $x + 1$ .

Factor $x + 1$ out of $x (x + 1)$ .

$\frac{2 x - 1}{x + 1} \cdot \frac{(x + 1) x}{3 x^{2}}$

Cancel the common factor.

$\frac{2 x - 1}{x + 1} \cdot \frac{(x + 1) x}{3 x^{2}}$

Rewrite the expression.

$(2 x - 1) \frac{x}{3 x^{2}}$

Step 4

Cancel the common factor of $x$ and $x^{2}$ .

Raise $x$ to the power of $1$ .

$(2 x - 1) \frac{x^{1}}{3 x^{2}}$

Factor $x$ out of $x^{1}$ .

$(2 x - 1) \frac{x \cdot 1}{3 x^{2}}$

Cancel the common factors.

Factor $x$ out of $3 x^{2}$ .

$(2 x - 1) \frac{x \cdot 1}{x (3 x)}$

Cancel the common factor.

$(2 x - 1) \frac{x \cdot 1}{x (3 x)}$

Rewrite the expression.

$(2 x - 1) \frac{1}{3 x}$

Step 5

Multiply $2 x - 1$ by $\frac{1}{3 x}$ .

$\frac{2 x - 1}{3 x}$