Calculus Examples

$4 b - \frac{9}{20} b + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $b$ and $\frac{9}{20}$ .

$4 b - \frac{b \cdot 9}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 1.2

Move $9$ to the left of $b$ .

$4 b - \frac{9 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 2

To write $4 b$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$4 b \cdot \frac{20}{20} - \frac{9 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $4 b$ and $\frac{20}{20}$ .

$\frac{4 b \cdot 20}{20} - \frac{9 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{4 b \cdot 20 - 9 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Factor $b$ out of $4 b \cdot 20 - 9 b$ .

Tap for more steps...

Step 4.1.1.1

Factor $b$ out of $4 b \cdot 20$ .

$\frac{b (4 \cdot 20) - 9 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4.1.1.2

Factor $b$ out of $- 9 b$ .

$\frac{b (4 \cdot 20) + b \cdot - 9}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4.1.1.3

Factor $b$ out of $b (4 \cdot 20) + b \cdot - 9$ .

$\frac{b (4 \cdot 20 - 9)}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4.1.2

Multiply $4$ by $20$ .

$\frac{b (80 - 9)}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4.1.3

Subtract $9$ from $80$ .

$\frac{b \cdot 71}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 4.2

Move $71$ to the left of $b$ .

$\frac{71 b}{20} + 7 + \frac{1}{10} - \frac{9}{10 b}$

Step 5

To write $7$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{71 b}{20} + 7 \cdot \frac{20}{20} + \frac{1}{10} - \frac{9}{10 b}$

Step 6

Combine $7$ and $\frac{20}{20}$ .

$\frac{71 b}{20} + \frac{7 \cdot 20}{20} + \frac{1}{10} - \frac{9}{10 b}$

Step 7

Combine the numerators over the common denominator.

$\frac{71 b + 7 \cdot 20}{20} + \frac{1}{10} - \frac{9}{10 b}$

Step 8

Multiply $7$ by $20$ .

$\frac{71 b + 140}{20} + \frac{1}{10} - \frac{9}{10 b}$

Step 9

Find the common denominator.

Tap for more steps...

Step 9.1

Multiply $\frac{71 b + 140}{20}$ by $\frac{b}{b}$ .

$\frac{71 b + 140}{20} \cdot \frac{b}{b} + \frac{1}{10} - \frac{9}{10 b}$

Step 9.2

Multiply $\frac{71 b + 140}{20}$ by $\frac{b}{b}$ .

$\frac{(71 b + 140) b}{20 b} + \frac{1}{10} - \frac{9}{10 b}$

Step 9.3

Multiply $\frac{1}{10}$ by $\frac{2 b}{2 b}$ .

$\frac{(71 b + 140) b}{20 b} + \frac{1}{10} \cdot \frac{2 b}{2 b} - \frac{9}{10 b}$

Step 9.4

Multiply $\frac{1}{10}$ by $\frac{2 b}{2 b}$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{10 (2 b)} - \frac{9}{10 b}$

Step 9.5

Multiply $\frac{9}{10 b}$ by $\frac{2}{2}$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{10 (2 b)} - (\frac{9}{10 b} \cdot \frac{2}{2})$

Step 9.6

Multiply $\frac{9}{10 b}$ by $\frac{2}{2}$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{10 (2 b)} - \frac{9 \cdot 2}{10 b \cdot 2}$

Step 9.7

Reorder the factors of $10 (2 b)$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{2 \cdot 10 b} - \frac{9 \cdot 2}{10 b \cdot 2}$

Step 9.8

Multiply $2$ by $10$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{20 b} - \frac{9 \cdot 2}{10 b \cdot 2}$

Step 9.9

Reorder the factors of $10 b \cdot 2$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{20 b} - \frac{9 \cdot 2}{2 \cdot 10 b}$

Step 9.10

Multiply $2$ by $10$ .

$\frac{(71 b + 140) b}{20 b} + \frac{2 b}{20 b} - \frac{9 \cdot 2}{20 b}$

Step 10

Combine the numerators over the common denominator.

$\frac{(71 b + 140) b + 2 b - 9 \cdot 2}{20 b}$

Step 11

Simplify each term.

Tap for more steps...

Step 11.1

Apply the distributive property.

$\frac{71 b \cdot b + 140 b + 2 b - 9 \cdot 2}{20 b}$

Step 11.2

Multiply $b$ by $b$ by adding the exponents.

Tap for more steps...

Step 11.2.1

Move $b$ .

$\frac{71 (b \cdot b) + 140 b + 2 b - 9 \cdot 2}{20 b}$

Step 11.2.2

Multiply $b$ by $b$ .

$\frac{71 b^{2} + 140 b + 2 b - 9 \cdot 2}{20 b}$

Step 11.3

Multiply $- 9$ by $2$ .

$\frac{71 b^{2} + 140 b + 2 b - 18}{20 b}$

Step 12

Add $140 b$ and $2 b$ .

$\frac{71 b^{2} + 142 b - 18}{20 b}$