Finite Math Examples

$\frac{- 3 x + 3 x^{2}}{- 24 x + 24}$

Step 1

Factor $3 x$ out of $- 3 x + 3 x^{2}$ .

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Step 1.1

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

$\frac{3 x (- 1) + 3 x^{2}}{- 24 x + 24}$

Step 1.2

Factor $3 x$ out of $3 x^{2}$ .

$\frac{3 x (- 1) + 3 x (x)}{- 24 x + 24}$

Step 1.3

Factor $3 x$ out of $3 x (- 1) + 3 x (x)$ .

$\frac{3 x (- 1 + x)}{- 24 x + 24}$

$\frac{3 x (- 1 + x)}{- 24 x + 24}$

Step 2

Factor $24$ out of $- 24 x + 24$ .

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Step 2.1

Factor $24$ out of $- 24 x$ .

$\frac{3 x (- 1 + x)}{24 (- x) + 24}$

Step 2.2

Factor $24$ out of $24$ .

$\frac{3 x (- 1 + x)}{24 (- x) + 24 (1)}$

Step 2.3

Factor $24$ out of $24 (- x) + 24 (1)$ .

$\frac{3 x (- 1 + x)}{24 (- x + 1)}$

$\frac{3 x (- 1 + x)}{24 (- x + 1)}$

Step 3

Cancel the common factor of $3$ and $24$ .

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Step 3.1

Factor $3$ out of $3 x (- 1 + x)$ .

$\frac{3 (x (- 1 + x))}{24 (- x + 1)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $24 (- x + 1)$ .

$\frac{3 (x (- 1 + x))}{3 (8 (- x + 1))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (x (- 1 + x))}{3 (8 (- x + 1))}$

Step 3.2.3

Rewrite the expression.

$\frac{x (- 1 + x)}{8 (- x + 1)}$

$\frac{x (- 1 + x)}{8 (- x + 1)}$

$\frac{x (- 1 + x)}{8 (- x + 1)}$

Step 4

Cancel the common factor of $- 1 + x$ and $- x + 1$ .

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Step 4.1

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

$\frac{x (- 1 (1) + x)}{8 (- x + 1)}$

Step 4.2

Factor $- 1$ out of $x$ .

$\frac{x (- 1 (1) - 1 (- x))}{8 (- x + 1)}$

Step 4.3

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

$\frac{x (- 1 (1 - x))}{8 (- x + 1)}$

Step 4.4

Reorder terms.

$\frac{x (- 1 (- x + 1))}{8 (- x + 1)}$

Step 4.5

Cancel the common factor.

$\frac{x (- 1 (- x + 1))}{8 (- x + 1)}$

Step 4.6

Rewrite the expression.

$\frac{x \cdot (- 1)}{8}$

$\frac{x \cdot (- 1)}{8}$

Step 5

Simplify the expression.

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Step 5.1

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{8}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{x}{8}$

$- \frac{x}{8}$

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