Basic Math Examples

$\frac{11}{4} \cdot 3^{n + 1} - \frac{3}{4} - \frac{n + 1}{2}$

Step 1

Combine $\frac{11}{4}$ and $3^{n + 1}$ .

$\frac{11 \cdot 3^{n + 1}}{4} - \frac{3}{4} - \frac{n + 1}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{11 \cdot 3^{n + 1} - 3}{4} - \frac{n + 1}{2}$

Step 3

To write $- \frac{n + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 \cdot 3^{n + 1} - 3}{4} - \frac{n + 1}{2} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{n + 1}{2}$ by $\frac{2}{2}$ .

$\frac{11 \cdot 3^{n + 1} - 3}{4} - \frac{(n + 1) \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{11 \cdot 3^{n + 1} - 3}{4} - \frac{(n + 1) \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 \cdot 3^{n + 1} - 3 - (n + 1) \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{11 \cdot 3^{n + 1} - 3 + (- n - 1 \cdot 1) \cdot 2}{4}$

Step 6.2

Multiply $- 1$ by $1$ .

$\frac{11 \cdot 3^{n + 1} - 3 + (- n - 1) \cdot 2}{4}$

Step 6.3

Apply the distributive property.

$\frac{11 \cdot 3^{n + 1} - 3 - n \cdot 2 - 1 \cdot 2}{4}$

Step 6.4

Multiply $2$ by $- 1$ .

$\frac{11 \cdot 3^{n + 1} - 3 - 2 n - 1 \cdot 2}{4}$

Step 6.5

Multiply $- 1$ by $2$ .

$\frac{11 \cdot 3^{n + 1} - 3 - 2 n - 2}{4}$

Step 6.6

Subtract $2$ from $- 3$ .

$\frac{11 \cdot 3^{n + 1} - 2 n - 5}{4}$

Step 6.7

Reorder terms.

$\frac{- 2 n + 11 \cdot 3^{n + 1} - 5}{4}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 2 n$ .

$\frac{- (2 n) + 11 \cdot 3^{n + 1} - 5}{4}$

Step 7.2

Factor $- 1$ out of $11 \cdot 3^{n + 1}$ .

$\frac{- (2 n) - (- 11 \cdot 3^{n + 1}) - 5}{4}$

Step 7.3

Factor $- 1$ out of $- (2 n) - (- 11 \cdot 3^{n + 1})$ .

$\frac{- (2 n - 11 \cdot 3^{n + 1}) - 5}{4}$

Step 7.4

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (2 n - 11 \cdot 3^{n + 1}) - 1 (5)}{4}$

Step 7.5

Factor $- 1$ out of $- (2 n - 11 \cdot 3^{n + 1}) - 1 (5)$ .

$\frac{- (2 n - 11 \cdot 3^{n + 1} + 5)}{4}$

Step 7.6

Simplify the expression.

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Step 7.6.1

Rewrite $- (2 n - 11 \cdot 3^{n + 1} + 5)$ as $- 1 (2 n - 11 \cdot 3^{n + 1} + 5)$ .

$\frac{- 1 (2 n - 11 \cdot 3^{n + 1} + 5)}{4}$

Step 7.6.2

Move the negative in front of the fraction.

$- \frac{2 n - 11 \cdot 3^{n + 1} + 5}{4}$