Algebra Examples

$\frac{5 x}{x - 7} + \frac{2 x}{4 x - 28}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ and $4 x - 28$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

$\frac{5 x}{x - 7} + \frac{2 (x)}{4 x - 28}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4 x$ .

$\frac{5 x}{x - 7} + \frac{2 (x)}{2 (2 x) - 28}$

Step 1.1.2.2

Factor $2$ out of $- 28$ .

$\frac{5 x}{x - 7} + \frac{2 x}{2 (2 x) + 2 \cdot - 14}$

Step 1.1.2.3

Factor $2$ out of $2 (2 x) + 2 (- 14)$ .

$\frac{5 x}{x - 7} + \frac{2 (x)}{2 (2 x - 14)}$

Step 1.1.2.4

Cancel the common factor.

$\frac{5 x}{x - 7} + \frac{2 x}{2 (2 x - 14)}$

Step 1.1.2.5

Rewrite the expression.

$\frac{5 x}{x - 7} + \frac{x}{2 x - 14}$

Step 1.2

Factor $2$ out of $2 x - 14$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$\frac{5 x}{x - 7} + \frac{x}{2 (x) - 14}$

Step 1.2.2

Factor $2$ out of $- 14$ .

$\frac{5 x}{x - 7} + \frac{x}{2 x + 2 \cdot - 7}$

Step 1.2.3

Factor $2$ out of $2 x + 2 \cdot - 7$ .

$\frac{5 x}{x - 7} + \frac{x}{2 (x - 7)}$

Step 2

To write $\frac{5 x}{x - 7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{x - 7} \cdot \frac{2}{2} + \frac{x}{2 (x - 7)}$

Step 3

Write each expression with a common denominator of $(x - 7) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 x}{x - 7}$ by $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{(x - 7) \cdot 2} + \frac{x}{2 (x - 7)}$

Step 3.2

Reorder the factors of $(x - 7) \cdot 2$ .

$\frac{5 x \cdot 2}{2 (x - 7)} + \frac{x}{2 (x - 7)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + x}{2 (x - 7)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $x$ out of $5 x \cdot 2 + x$ .

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Step 5.1.1

Factor $x$ out of $5 x \cdot 2$ .

$\frac{x (5 \cdot 2) + x}{2 (x - 7)}$

Step 5.1.2

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

$\frac{x (5 \cdot 2) + x^{1}}{2 (x - 7)}$

Step 5.1.3

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

$\frac{x (5 \cdot 2) + x \cdot 1}{2 (x - 7)}$

Step 5.1.4

Factor $x$ out of $x (5 \cdot 2) + x \cdot 1$ .

$\frac{x (5 \cdot 2 + 1)}{2 (x - 7)}$

Step 5.2

Multiply $5$ by $2$ .

$\frac{x (10 + 1)}{2 (x - 7)}$

Step 5.3

Add $10$ and $1$ .

$\frac{x \cdot 11}{2 (x - 7)}$

Step 6

Move $11$ to the left of $x$ .

$\frac{11 x}{2 (x - 7)}$