Algebra Examples

$\frac{6 (\frac{7 x + 5}{3 x - 6}) + 5}{3 (\frac{7 x + 5}{3 x - 6}) - 7}$

Step 1

Simplify with factoring out.

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Step 1.1

Factor $3$ out of $3 x - 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{6 \frac{7 x + 5}{3 (x) - 6} + 5}{3 \frac{7 x + 5}{3 x - 6} - 7}$

Step 1.1.2

Factor $3$ out of $- 6$ .

$\frac{6 \frac{7 x + 5}{3 x + 3 \cdot - 2} + 5}{3 \frac{7 x + 5}{3 x - 6} - 7}$

Step 1.1.3

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

$\frac{6 \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 x - 6} - 7}$

Step 1.2

Factor $3$ out of $3 x - 6$ .

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Step 1.2.1

Factor $3$ out of $3 x$ .

$\frac{6 \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 (x) - 6} - 7}$

Step 1.2.2

Factor $3$ out of $- 6$ .

$\frac{6 \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 x + 3 \cdot - 2} - 7}$

Step 1.2.3

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

$\frac{6 \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2

Simplify the numerator.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Factor $3$ out of $6$ .

$\frac{3 (2) \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.1.2

Cancel the common factor.

$\frac{3 \cdot 2 \frac{7 x + 5}{3 (x - 2)} + 5}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.1.3

Rewrite the expression.

$\frac{2 \frac{7 x + 5}{x - 2} + 5}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.2

Combine $2$ and $\frac{7 x + 5}{x - 2}$ .

$\frac{\frac{2 (7 x + 5)}{x - 2} + 5}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.3

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

$\frac{\frac{2 (7 x + 5)}{x - 2} + \frac{5 (x - 2)}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{2 (7 x + 5) + 5 (x - 2)}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.5

Reorder terms.

$\frac{\frac{5 (x - 2) + 2 (7 x + 5)}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6

Rewrite $\frac{5 (x - 2) + 2 (7 x + 5)}{x - 2}$ in a factored form.

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Step 2.6.1

Apply the distributive property.

$\frac{\frac{5 x + 5 \cdot - 2 + 2 (7 x + 5)}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.2

Multiply $5$ by $- 2$ .

$\frac{\frac{5 x - 10 + 2 (7 x + 5)}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.3

Apply the distributive property.

$\frac{\frac{5 x - 10 + 2 (7 x) + 2 \cdot 5}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.4

Multiply $7$ by $2$ .

$\frac{\frac{5 x - 10 + 14 x + 2 \cdot 5}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.5

Multiply $2$ by $5$ .

$\frac{\frac{5 x - 10 + 14 x + 10}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.6

Add $5 x$ and $14 x$ .

$\frac{\frac{19 x - 10 + 10}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.7

Add $- 10$ and $10$ .

$\frac{\frac{19 x + 0}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 2.6.8

Add $19 x$ and $0$ .

$\frac{\frac{19 x}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 3

Simplify the denominator.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{\frac{19 x}{x - 2}}{3 \frac{7 x + 5}{3 (x - 2)} - 7}$

Step 3.1.2

Rewrite the expression.

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5}{x - 2} - 7}$

Step 3.2

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

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5}{x - 2} - 7 \cdot \frac{x - 2}{x - 2}}$

Step 3.3

Combine $- 7$ and $\frac{x - 2}{x - 2}$ .

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5}{x - 2} + \frac{- 7 (x - 2)}{x - 2}}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5 - 7 (x - 2)}{x - 2}}$

Step 3.5

Rewrite $\frac{7 x + 5 - 7 (x - 2)}{x - 2}$ in a factored form.

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Step 3.5.1

Apply the distributive property.

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5 - 7 x - 7 \cdot - 2}{x - 2}}$

Step 3.5.2

Multiply $- 7$ by $- 2$ .

$\frac{\frac{19 x}{x - 2}}{\frac{7 x + 5 - 7 x + 14}{x - 2}}$

Step 3.5.3

Subtract $7 x$ from $7 x$ .

$\frac{\frac{19 x}{x - 2}}{\frac{0 + 5 + 14}{x - 2}}$

Step 3.5.4

Add $0$ and $5$ .

$\frac{\frac{19 x}{x - 2}}{\frac{5 + 14}{x - 2}}$

Step 3.5.5

Add $5$ and $14$ .

$\frac{\frac{19 x}{x - 2}}{\frac{19}{x - 2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{19 x}{x - 2} \cdot \frac{x - 2}{19}$

Step 5

Cancel the common factor of $19$ .

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Step 5.1

Factor $19$ out of $19 x$ .

$\frac{19 (x)}{x - 2} \cdot \frac{x - 2}{19}$

Step 5.2

Cancel the common factor.

$\frac{19 x}{x - 2} \cdot \frac{x - 2}{19}$

Step 5.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $x - 2$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$x$