Calculus Examples

$\frac{17}{3} - \frac{{(\frac{17}{3})}^{3} - 4}{3 {(\frac{17}{3})}^{2}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify the numerator.

Tap for more steps...

Step 1.1.1

Apply the product rule to $\frac{17}{3}$ .

$\frac{17}{3} - \frac{\frac{17^{3}}{3^{3}} - 4}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.2

Raise $17$ to the power of $3$ .

$\frac{17}{3} - \frac{\frac{4913}{3^{3}} - 4}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.3

Raise $3$ to the power of $3$ .

$\frac{17}{3} - \frac{\frac{4913}{27} - 4}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.4

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{17}{3} - \frac{\frac{4913}{27} - 4 \cdot \frac{27}{27}}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.5

Combine $- 4$ and $\frac{27}{27}$ .

$\frac{17}{3} - \frac{\frac{4913}{27} + \frac{- 4 \cdot 27}{27}}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{17}{3} - \frac{\frac{4913 - 4 \cdot 27}{27}}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.7

Simplify the numerator.

Tap for more steps...

Step 1.1.7.1

Multiply $- 4$ by $27$ .

$\frac{17}{3} - \frac{\frac{4913 - 108}{27}}{3 {(\frac{17}{3})}^{2}}$

Step 1.1.7.2

Subtract $108$ from $4913$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{3 {(\frac{17}{3})}^{2}}$

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

Apply the product rule to $\frac{17}{3}$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{3 \frac{17^{2}}{3^{2}}}$

Step 1.2.2

Raise $17$ to the power of $2$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{3 \frac{289}{3^{2}}}$

Step 1.2.3

Raise $3$ to the power of $2$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{3 (\frac{289}{9})}$

Step 1.3

Combine $3$ and $\frac{289}{9}$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{3 \cdot 289}{9}}$

Step 1.4

Multiply $3$ by $289$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{867}{9}}$

Step 1.5

Cancel the common factor of $867$ and $9$ .

Tap for more steps...

Step 1.5.1

Factor $3$ out of $867$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{3 (289)}{9}}$

Step 1.5.2

Cancel the common factors.

Tap for more steps...

Step 1.5.2.1

Factor $3$ out of $9$ .

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{3 \cdot 289}{3 \cdot 3}}$

Step 1.5.2.2

Cancel the common factor.

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{3 \cdot 289}{3 \cdot 3}}$

Step 1.5.2.3

Rewrite the expression.

$\frac{17}{3} - \frac{\frac{4805}{27}}{\frac{289}{3}}$

Step 1.6

Multiply the numerator by the reciprocal of the denominator.

$\frac{17}{3} - (\frac{4805}{27} \cdot \frac{3}{289})$

Step 1.7

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.7.1

Factor $3$ out of $27$ .

$\frac{17}{3} - (\frac{4805}{3 (9)} \cdot \frac{3}{289})$

Step 1.7.2

Cancel the common factor.

$\frac{17}{3} - (\frac{4805}{3 \cdot 9} \cdot \frac{3}{289})$

Step 1.7.3

Rewrite the expression.

$\frac{17}{3} - (\frac{4805}{9} \cdot \frac{1}{289})$

Step 1.8

Multiply $\frac{4805}{9}$ by $\frac{1}{289}$ .

$\frac{17}{3} - \frac{4805}{9 \cdot 289}$

Step 1.9

Multiply $9$ by $289$ .

$\frac{17}{3} - \frac{4805}{2601}$

Step 2

To write $\frac{17}{3}$ as a fraction with a common denominator, multiply by $\frac{867}{867}$ .

$\frac{17}{3} \cdot \frac{867}{867} - \frac{4805}{2601}$

Step 3

Write each expression with a common denominator of $2601$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{17}{3}$ by $\frac{867}{867}$ .

$\frac{17 \cdot 867}{3 \cdot 867} - \frac{4805}{2601}$

Step 3.2

Multiply $3$ by $867$ .

$\frac{17 \cdot 867}{2601} - \frac{4805}{2601}$

Step 4

Combine the numerators over the common denominator.

$\frac{17 \cdot 867 - 4805}{2601}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $17$ by $867$ .

$\frac{14739 - 4805}{2601}$

Step 5.2

Subtract $4805$ from $14739$ .

$\frac{9934}{2601}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9934}{2601}$

Decimal Form:

$3.81930026 \dots$

Mixed Number Form:

$3 \frac{2131}{2601}$