Algebra Examples

$\frac{5 x}{7 x} + \frac{10 x}{x^{2}}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Cancel the common factor.

$\frac{5 x}{7 x} + \frac{10 x}{x^{2}}$

Step 1.1.2

Rewrite the expression.

$\frac{5}{7} + \frac{10 x}{x^{2}}$

Step 1.2

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

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Step 1.2.1

Factor $x$ out of $10 x$ .

$\frac{5}{7} + \frac{x \cdot 10}{x^{2}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

$\frac{5}{7} + \frac{x \cdot 10}{x \cdot x}$

Step 1.2.2.2

Cancel the common factor.

$\frac{5}{7} + \frac{x \cdot 10}{x \cdot x}$

Step 1.2.2.3

Rewrite the expression.

$\frac{5}{7} + \frac{10}{x}$

Step 2

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

$\frac{5}{7} \cdot \frac{x}{x} + \frac{10}{x}$

Step 3

To write $\frac{10}{x}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5}{7} \cdot \frac{x}{x} + \frac{10}{x} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $7 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{5 x}{7 x} + \frac{10}{x} \cdot \frac{7}{7}$

Step 4.2

Multiply $\frac{10}{x}$ by $\frac{7}{7}$ .

$\frac{5 x}{7 x} + \frac{10 \cdot 7}{x \cdot 7}$

Step 4.3

Reorder the factors of $x \cdot 7$ .

$\frac{5 x}{7 x} + \frac{10 \cdot 7}{7 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 x + 10 \cdot 7}{7 x}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $5$ out of $5 x + 10 \cdot 7$ .

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Step 6.1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 10 \cdot 7}{7 x}$

Step 6.1.2

Factor $5$ out of $10 \cdot 7$ .

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

Step 6.1.3

Factor $5$ out of $5 (x) + 5 (2 \cdot 7)$ .

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

Step 6.2

Multiply $2$ by $7$ .

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