Finite Math Examples

$\frac{- 18 + 2 x}{\frac{3}{\frac{25 x - 225}{9}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(- 18 + 2 x) \frac{\frac{25 x - 225}{9}}{3}$

Step 2

Factor $25$ out of $25 x - 225$ .

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Step 2.1

Factor $25$ out of $25 x$ .

$(- 18 + 2 x) \frac{\frac{25 (x) - 225}{9}}{3}$

Step 2.2

Factor $25$ out of $- 225$ .

$(- 18 + 2 x) \frac{\frac{25 x + 25 \cdot - 9}{9}}{3}$

Step 2.3

Factor $25$ out of $25 x + 25 \cdot - 9$ .

$(- 18 + 2 x) \frac{\frac{25 (x - 9)}{9}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$(- 18 + 2 x) (\frac{25 (x - 9)}{9} \cdot \frac{1}{3})$

Step 4

Multiply $\frac{25 (x - 9)}{9} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply $\frac{25 (x - 9)}{9}$ by $\frac{1}{3}$ .

$(- 18 + 2 x) \frac{25 (x - 9)}{9 \cdot 3}$

Step 4.2

Multiply $9$ by $3$ .

$(- 18 + 2 x) \frac{25 (x - 9)}{27}$

Step 5

Apply the distributive property.

$- 18 \frac{25 (x - 9)}{27} + 2 x \frac{25 (x - 9)}{27}$

Step 6

Cancel the common factor of $9$ .

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Step 6.1

Factor $9$ out of $- 18$ .

$9 (- 2) \frac{25 (x - 9)}{27} + 2 x \frac{25 (x - 9)}{27}$

Step 6.2

Factor $9$ out of $27$ .

$9 \cdot - 2 \frac{25 (x - 9)}{9 \cdot 3} + 2 x \frac{25 (x - 9)}{27}$

Step 6.3

Cancel the common factor.

$9 \cdot - 2 \frac{25 (x - 9)}{9 \cdot 3} + 2 x \frac{25 (x - 9)}{27}$

Step 6.4

Rewrite the expression.

$- 2 \frac{25 (x - 9)}{3} + 2 x \frac{25 (x - 9)}{27}$

Step 7

Combine $- 2$ and $\frac{25 (x - 9)}{3}$ .

$\frac{- 2 (25 (x - 9))}{3} + 2 x \frac{25 (x - 9)}{27}$

Step 8

Multiply $25$ by $- 2$ .

$\frac{- 50 (x - 9)}{3} + 2 x \frac{25 (x - 9)}{27}$

Step 9

Multiply $2 x \frac{25 (x - 9)}{27}$ .

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Step 9.1

Combine $2$ and $\frac{25 (x - 9)}{27}$ .

$\frac{- 50 (x - 9)}{3} + x \frac{2 (25 (x - 9))}{27}$

Step 9.2

Multiply $25$ by $2$ .

$\frac{- 50 (x - 9)}{3} + x \frac{50 (x - 9)}{27}$

Step 9.3

Combine $x$ and $\frac{50 (x - 9)}{27}$ .

$\frac{- 50 (x - 9)}{3} + \frac{x (50 (x - 9))}{27}$

Step 10

Simplify each term.

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Step 10.1

Move the negative in front of the fraction.

$- \frac{50 (x - 9)}{3} + \frac{x (50 (x - 9))}{27}$

Step 10.2

Remove unnecessary parentheses.

$- \frac{50 (x - 9)}{3} + \frac{x \cdot 50 (x - 9)}{27}$

Step 10.3

Move $50$ to the left of $x$ .

$- \frac{50 (x - 9)}{3} + \frac{50 x (x - 9)}{27}$

Step 11

To write $- \frac{50 (x - 9)}{3}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{50 (x - 9)}{3} \cdot \frac{9}{9} + \frac{50 x (x - 9)}{27}$

Step 12

Write each expression with a common denominator of $27$ , by multiplying each by an appropriate factor of $1$ .

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Step 12.1

Multiply $\frac{50 (x - 9)}{3}$ by $\frac{9}{9}$ .

$- \frac{50 (x - 9) \cdot 9}{3 \cdot 9} + \frac{50 x (x - 9)}{27}$

Step 12.2

Multiply $3$ by $9$ .

$- \frac{50 (x - 9) \cdot 9}{27} + \frac{50 x (x - 9)}{27}$

Step 13

Combine the numerators over the common denominator.

$\frac{- 50 (x - 9) \cdot 9 + 50 x (x - 9)}{27}$

Step 14

Simplify the numerator.

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Step 14.1

Factor $50 (x - 9)$ out of $- 50 (x - 9) \cdot 9 + 50 x (x - 9)$ .

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Step 14.1.1

Factor $50 (x - 9)$ out of $- 50 (x - 9) \cdot 9$ .

$\frac{50 (x - 9) (- 1 \cdot 9) + 50 x (x - 9)}{27}$

Step 14.1.2

Factor $50 (x - 9)$ out of $50 x (x - 9)$ .

$\frac{50 (x - 9) (- 1 \cdot 9) + 50 (x - 9) (x)}{27}$

Step 14.1.3

Factor $50 (x - 9)$ out of $50 (x - 9) (- 1 \cdot 9) + 50 (x - 9) (x)$ .

$\frac{50 (x - 9) (- 1 \cdot 9 + x)}{27}$

Step 14.2

Combine exponents.

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Step 14.2.1

Multiply $- 1$ by $9$ .

$\frac{50 (x - 9) (- 9 + x)}{27}$

Step 14.2.2

Reorder terms.

$\frac{50 (x - 9) (x - 9)}{27}$

Step 14.2.3

Raise $x - 9$ to the power of $1$ .

$\frac{50 ({(x - 9)}^{1} (x - 9))}{27}$

Step 14.2.4

Raise $x - 9$ to the power of $1$ .

$\frac{50 ({(x - 9)}^{1} {(x - 9)}^{1})}{27}$

Step 14.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{50 {(x - 9)}^{1 + 1}}{27}$

Step 14.2.6

Add $1$ and $1$ .

$\frac{50 {(x - 9)}^{2}}{27}$