Calculus Examples

$\frac{200}{q} + 2 + 4 q + 144$

Step 1

Find the common denominator.

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Step 1.1

Write $2$ as a fraction with denominator $1$ .

$\frac{200}{q} + \frac{2}{1} + 4 q + 144$

Step 1.2

Multiply $\frac{2}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2}{1} \cdot \frac{q}{q} + 4 q + 144$

Step 1.3

Multiply $\frac{2}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2 q}{q} + 4 q + 144$

Step 1.4

Write $4 q$ as a fraction with denominator $1$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q}{1} + 144$

Step 1.5

Multiply $\frac{4 q}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q}{1} \cdot \frac{q}{q} + 144$

Step 1.6

Multiply $\frac{4 q}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q \cdot q}{q} + 144$

Step 1.7

Write $144$ as a fraction with denominator $1$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q \cdot q}{q} + \frac{144}{1}$

Step 1.8

Multiply $\frac{144}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q \cdot q}{q} + \frac{144}{1} \cdot \frac{q}{q}$

Step 1.9

Multiply $\frac{144}{1}$ by $\frac{q}{q}$ .

$\frac{200}{q} + \frac{2 q}{q} + \frac{4 q \cdot q}{q} + \frac{144 q}{q}$

Step 2

Combine the numerators over the common denominator.

$\frac{200 + 2 q + 4 q \cdot q + 144 q}{q}$

Step 3

Multiply $q$ by $q$ by adding the exponents.

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Step 3.1

Move $q$ .

$\frac{200 + 2 q + 4 (q \cdot q) + 144 q}{q}$

Step 3.2

Multiply $q$ by $q$ .

$\frac{200 + 2 q + 4 q^{2} + 144 q}{q}$

Step 4

Add $2 q$ and $144 q$ .

$\frac{200 + 4 q^{2} + 146 q}{q}$

Step 5

Move $200$ .

$\frac{4 q^{2} + 146 q + 200}{q}$

Step 6

Factor $2$ out of $4 q^{2} + 146 q + 200$ .

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Step 6.1

Factor $2$ out of $4 q^{2}$ .

$\frac{2 (2 q^{2}) + 146 q + 200}{q}$

Step 6.2

Factor $2$ out of $146 q$ .

$\frac{2 (2 q^{2}) + 2 (73 q) + 200}{q}$

Step 6.3

Factor $2$ out of $200$ .

$\frac{2 (2 q^{2}) + 2 (73 q) + 2 (100)}{q}$

Step 6.4

Factor $2$ out of $2 (2 q^{2}) + 2 (73 q)$ .

$\frac{2 (2 q^{2} + 73 q) + 2 (100)}{q}$

Step 6.5

Factor $2$ out of $2 (2 q^{2} + 73 q) + 2 (100)$ .

$\frac{2 (2 q^{2} + 73 q + 100)}{q}$