Algebra Examples

$\frac{x^{2} - 9 x}{45 x - 5 x^{2}}$

Step 1

Factor $x$ out of $x^{2} - 9 x$ .

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Step 1.1

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

$\frac{x \cdot x - 9 x}{45 x - 5 x^{2}}$

Step 1.2

Factor $x$ out of $- 9 x$ .

$\frac{x \cdot x + x \cdot - 9}{45 x - 5 x^{2}}$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot - 9$ .

$\frac{x (x - 9)}{45 x - 5 x^{2}}$

$\frac{x (x - 9)}{45 x - 5 x^{2}}$

Step 2

Factor $5 x$ out of $45 x - 5 x^{2}$ .

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Step 2.1

Factor $5 x$ out of $45 x$ .

$\frac{x (x - 9)}{5 x (9) - 5 x^{2}}$

Step 2.2

Factor $5 x$ out of $- 5 x^{2}$ .

$\frac{x (x - 9)}{5 x (9) + 5 x (- x)}$

Step 2.3

Factor $5 x$ out of $5 x (9) + 5 x (- x)$ .

$\frac{x (x - 9)}{5 x (9 - x)}$

$\frac{x (x - 9)}{5 x (9 - x)}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x (x - 9)}{5 x (9 - x)}$

Step 3.2

Rewrite the expression.

$\frac{x - 9}{5 (9 - x)}$

$\frac{x - 9}{5 (9 - x)}$

Step 4

Cancel the common factor of $x - 9$ and $9 - x$ .

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Step 4.1

Factor $- 1$ out of $x$ .

$\frac{- 1 (- x) - 9}{5 (9 - x)}$

Step 4.2

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 (- x) - 1 (9)}{5 (9 - x)}$

Step 4.3

Factor $- 1$ out of $- 1 (- x) - 1 (9)$ .

$\frac{- 1 (- x + 9)}{5 (9 - x)}$

Step 4.4

Reorder terms.

$\frac{- 1 (- x + 9)}{5 (- x + 9)}$

Step 4.5

Cancel the common factor.

$\frac{- 1 (- x + 9)}{5 (- x + 9)}$

Step 4.6

Rewrite the expression.

$\frac{- 1}{5}$

$\frac{- 1}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{5}$

Decimal Form:

$- 0.2$

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