Calculus Examples

$\frac{3 {(5)}^{2} (- 18)}{2 {(5)}^{3} - (- 18)}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $- 18$ and $2 {(5)}^{3} - (- 18)$ .

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Step 1.1.1

Reorder terms.

$\frac{3 {(5)}^{2} (- 18)}{2 {(5)}^{3} - 18 \cdot - 1}$

Step 1.1.2

Factor $2$ out of $3 {(5)}^{2} (- 18)$ .

$\frac{2 (3 {(5)}^{2} \cdot (- 9))}{2 {(5)}^{3} - 18 \cdot - 1}$

Step 1.1.3

Cancel the common factors.

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Step 1.1.3.1

Factor $2$ out of $2 {(5)}^{3}$ .

$\frac{2 (3 {(5)}^{2} \cdot (- 9))}{2 ({(5)}^{3}) - 18 \cdot - 1}$

Step 1.1.3.2

Factor $2$ out of $- 18 \cdot - 1$ .

$\frac{2 (3 {(5)}^{2} \cdot (- 9))}{2 ({(5)}^{3}) + 2 (- 9 \cdot - 1)}$

Step 1.1.3.3

Factor $2$ out of $2 ({(5)}^{3}) + 2 (- 9 \cdot - 1)$ .

$\frac{2 (3 {(5)}^{2} \cdot (- 9))}{2 ({(5)}^{3} - 9 \cdot - 1)}$

Step 1.1.3.4

Cancel the common factor.

$\frac{2 (3 {(5)}^{2} \cdot (- 9))}{2 ({(5)}^{3} - 9 \cdot - 1)}$

Step 1.1.3.5

Rewrite the expression.

$\frac{3 {(5)}^{2} \cdot (- 9)}{{(5)}^{3} - 9 \cdot - 1}$

Step 1.2

Multiply $- 9$ by $3$ .

$\frac{- 27 \cdot 5^{2}}{5^{3} - 9 \cdot - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $5$ to the power of $3$ .

$\frac{- 27 \cdot 5^{2}}{125 - 9 \cdot - 1}$

Step 2.2

Multiply $- 9$ by $- 1$ .

$\frac{- 27 \cdot 5^{2}}{125 + 9}$

Step 2.3

Add $125$ and $9$ .

$\frac{- 27 \cdot 5^{2}}{134}$

Step 3

Simplify the expression.

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Step 3.1

Raise $5$ to the power of $2$ .

$\frac{- 27 \cdot 25}{134}$

Step 3.2

Multiply $- 27$ by $25$ .

$\frac{- 675}{134}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{675}{134}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{675}{134}$

Decimal Form:

$- 5.03731343 \dots$

Mixed Number Form:

$- 5 \frac{5}{134}$