Simplify (x^2+4x)/(x-3)*(2x-6)/(10x)

$\frac{x^{2} + 4 x}{x - 3} \cdot \frac{2 x - 6}{10 x}$

Step 1

Factor $x$ out of $x^{2} + 4 x$ .

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

$\frac{x \cdot x + 4 x}{x - 3} \cdot \frac{2 x - 6}{10 x}$

Factor $x$ out of $4 x$ .

$\frac{x \cdot x + x \cdot 4}{x - 3} \cdot \frac{2 x - 6}{10 x}$

Factor $x$ out of $x \cdot x + x \cdot 4$ .

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 x - 6}{10 x}$

Step 2

Factor $2$ out of $2 x - 6$ .

Factor $2$ out of $2 x$ .

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 (x) - 6}{10 x}$

Factor $2$ out of $- 6$ .

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 x + 2 \cdot - 3}{10 x}$

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 (x - 3)}{10 x}$

Step 3

Cancel the common factor of $x$ .

Factor $x$ out of $10 x$ .

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 (x - 3)}{x \cdot 10}$

Cancel the common factor.

$\frac{x (x + 4)}{x - 3} \cdot \frac{2 (x - 3)}{x \cdot 10}$

Rewrite the expression.

$\frac{x + 4}{x - 3} \cdot \frac{2 (x - 3)}{10}$

Step 4

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $2 (x - 3)$ .

$\frac{x + 4}{x - 3} \cdot \frac{(x - 3) \cdot 2}{10}$

Cancel the common factor.

$\frac{x + 4}{x - 3} \cdot \frac{(x - 3) \cdot 2}{10}$

Rewrite the expression.

$(x + 4) \cdot \frac{2}{10}$

Step 5

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2$ .

$(x + 4) \cdot \frac{2 (1)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$(x + 4) \cdot \frac{2 \cdot 1}{2 \cdot 5}$

Cancel the common factor.

$(x + 4) \cdot \frac{2 \cdot 1}{2 \cdot 5}$

Rewrite the expression.

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

Step 6

Apply the distributive property.

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

Step 7

Combine $x$ and $\frac{1}{5}$ .

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

Step 8

Combine $4$ and $\frac{1}{5}$ .

$\frac{x}{5} + \frac{4}{5}$

Step 9

Combine the numerators over the common denominator.

$\frac{x + 4}{5}$

Simplify (x^2+4x)/(x-3)*(2x-6)/(10x)

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