Precalculus Examples

$\frac{\frac{25}{12} + \frac{x + 1}{4}}{\frac{1}{18} - \frac{x + 1}{36}}$

Step 1

Multiply the numerator and denominator of the fraction by $36$ .

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Step 1.1

Multiply $\frac{\frac{25}{12} + \frac{x + 1}{4}}{\frac{1}{18} - \frac{x + 1}{36}}$ by $\frac{36}{36}$ .

$\frac{36}{36} \cdot \frac{\frac{25}{12} + \frac{x + 1}{4}}{\frac{1}{18} - \frac{x + 1}{36}}$

Step 1.2

Combine.

$\frac{36 (\frac{25}{12} + \frac{x + 1}{4})}{36 (\frac{1}{18} - \frac{x + 1}{36})}$

Step 2

Apply the distributive property.

$\frac{36 (\frac{25}{12}) + 36 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $12$ .

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Step 3.1.1

Factor $12$ out of $36$ .

$\frac{12 (3) \frac{25}{12} + 36 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.1.2

Cancel the common factor.

$\frac{12 \cdot 3 \frac{25}{12} + 36 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.1.3

Rewrite the expression.

$\frac{3 \cdot 25 + 36 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.2

Multiply $3$ by $25$ .

$\frac{75 + 36 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $36$ .

$\frac{75 + 4 (9) \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.3.2

Cancel the common factor.

$\frac{75 + 4 \cdot 9 \frac{x + 1}{4}}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.3.3

Rewrite the expression.

$\frac{75 + 9 (x + 1)}{36 (\frac{1}{18}) + 36 (- \frac{x + 1}{36})}$

Step 3.4

Cancel the common factor of $18$ .

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Step 3.4.1

Factor $18$ out of $36$ .

$\frac{75 + 9 (x + 1)}{18 (2) \frac{1}{18} + 36 (- \frac{x + 1}{36})}$

Step 3.4.2

Cancel the common factor.

$\frac{75 + 9 (x + 1)}{18 \cdot 2 \frac{1}{18} + 36 (- \frac{x + 1}{36})}$

Step 3.4.3

Rewrite the expression.

$\frac{75 + 9 (x + 1)}{2 + 36 (- \frac{x + 1}{36})}$

Step 3.5

Cancel the common factor of $36$ .

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Step 3.5.1

Move the leading negative in $- \frac{x + 1}{36}$ into the numerator.

$\frac{75 + 9 (x + 1)}{2 + 36 \frac{- (x + 1)}{36}}$

Step 3.5.2

Cancel the common factor.

$\frac{75 + 9 (x + 1)}{2 + 36 \frac{- (x + 1)}{36}}$

Step 3.5.3

Rewrite the expression.

$\frac{75 + 9 (x + 1)}{2 - (x + 1)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $3$ out of $75 + 9 (x + 1)$ .

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Step 4.1.1

Factor $3$ out of $75$ .

$\frac{3 (25) + 9 (x + 1)}{2 - (x + 1)}$

Step 4.1.2

Factor $3$ out of $9 (x + 1)$ .

$\frac{3 (25) + 3 (3 (x + 1))}{2 - (x + 1)}$

Step 4.1.3

Factor $3$ out of $3 (25) + 3 (3 (x + 1))$ .

$\frac{3 (25 + 3 (x + 1))}{2 - (x + 1)}$

Step 4.2

Apply the distributive property.

$\frac{3 (25 + 3 x + 3 \cdot 1)}{2 - (x + 1)}$

Step 4.3

Multiply $3$ by $1$ .

$\frac{3 (25 + 3 x + 3)}{2 - (x + 1)}$

Step 4.4

Add $25$ and $3$ .

$\frac{3 (3 x + 28)}{2 - (x + 1)}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the distributive property.

$\frac{3 (3 x + 28)}{2 - x - 1 \cdot 1}$

Step 5.2

Multiply $- 1$ by $1$ .

$\frac{3 (3 x + 28)}{2 - x - 1}$

Step 5.3

Subtract $1$ from $2$ .

$\frac{3 (3 x + 28)}{- x + 1}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- x$ .

$\frac{3 (3 x + 28)}{- (x) + 1}$

Step 6.2

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{3 (3 x + 28)}{- (x) - 1 (- 1)}$

Step 6.3

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

$\frac{3 (3 x + 28)}{- (x - 1)}$

Step 6.4

Rewrite negatives.

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Step 6.4.1

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

$\frac{3 (3 x + 28)}{- 1 (x - 1)}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{3 (3 x + 28)}{x - 1}$