Calculus Examples

$\frac{3 x - 6}{10 - 5 x}$

Step 1

Simplify terms.

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Step 1.1

Factor $3$ out of $3 x - 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{10 - 5 x}$

Step 1.1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{10 - 5 x}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{10 - 5 x}$

$\frac{3 (x - 2)}{10 - 5 x}$

Step 1.2

Factor $5$ out of $10 - 5 x$ .

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Step 1.2.1

Factor $5$ out of $10$ .

$\frac{3 (x - 2)}{5 (2) - 5 x}$

Step 1.2.2

Factor $5$ out of $- 5 x$ .

$\frac{3 (x - 2)}{5 (2) + 5 (- x)}$

Step 1.2.3

Factor $5$ out of $5 (2) + 5 (- x)$ .

$\frac{3 (x - 2)}{5 (2 - x)}$

$\frac{3 (x - 2)}{5 (2 - x)}$

Step 1.3

Cancel the common factor of $x - 2$ and $2 - x$ .

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Step 1.3.1

Factor $- 1$ out of $x$ .

$\frac{3 (- 1 (- x) - 2)}{5 (2 - x)}$

Step 1.3.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{3 (- 1 (- x) - 1 (2))}{5 (2 - x)}$

Step 1.3.3

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

$\frac{3 (- 1 (- x + 2))}{5 (2 - x)}$

Step 1.3.4

Reorder terms.

$\frac{3 (- 1 (- x + 2))}{5 (- x + 2)}$

Step 1.3.5

Cancel the common factor.

$\frac{3 (- 1 (- x + 2))}{5 (- x + 2)}$

Step 1.3.6

Rewrite the expression.

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

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

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

Step 2

Multiply $3$ by $- 1$ .

$\frac{- 3}{5}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$