Finite Math Examples

$1 - \frac{2}{\frac{x}{x - \frac{5}{6 x}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$1 - (2 \frac{x - \frac{5}{6 x}}{x})$

Step 2

Simplify the numerator.

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Step 2.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{6 x}{6 x}$ .

$1 - (2 \frac{x \cdot \frac{6 x}{6 x} - \frac{5}{6 x}}{x})$

Step 2.2

Combine $x$ and $\frac{6 x}{6 x}$ .

$1 - (2 \frac{\frac{x (6 x)}{6 x} - \frac{5}{6 x}}{x})$

Step 2.3

Combine the numerators over the common denominator.

$1 - (2 \frac{\frac{x (6 x) - 5}{6 x}}{x})$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Rewrite using the commutative property of multiplication.

$1 - (2 \frac{\frac{6 x \cdot x - 5}{6 x}}{x})$

Step 2.4.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.4.2.1

Move $x$ .

$1 - (2 \frac{\frac{6 (x \cdot x) - 5}{6 x}}{x})$

Step 2.4.2.2

Multiply $x$ by $x$ .

$1 - (2 \frac{\frac{6 x^{2} - 5}{6 x}}{x})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 - (2 (\frac{6 x^{2} - 5}{6 x} \cdot \frac{1}{x}))$

Step 4

Multiply $\frac{6 x^{2} - 5}{6 x} \cdot \frac{1}{x}$ .

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Step 4.1

Multiply $\frac{6 x^{2} - 5}{6 x}$ by $\frac{1}{x}$ .

$1 - (2 \frac{6 x^{2} - 5}{6 x \cdot x})$

Step 4.2

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

$1 - (2 \frac{6 x^{2} - 5}{6 (x^{1} x)})$

Step 4.3

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

$1 - (2 \frac{6 x^{2} - 5}{6 (x^{1} x^{1})})$

Step 4.4

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

$1 - (2 \frac{6 x^{2} - 5}{6 x^{1 + 1}})$

Step 4.5

Add $1$ and $1$ .

$1 - (2 \frac{6 x^{2} - 5}{6 x^{2}})$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $6 x^{2}$ .

$1 - (2 \frac{6 x^{2} - 5}{2 (3 x^{2})})$

Step 5.2

Cancel the common factor.

$1 - (2 \frac{6 x^{2} - 5}{2 (3 x^{2})})$

Step 5.3

Rewrite the expression.

$1 - \frac{6 x^{2} - 5}{3 x^{2}}$

Step 6

Write $1$ as a fraction with a common denominator.

$\frac{3 x^{2}}{3 x^{2}} - \frac{6 x^{2} - 5}{3 x^{2}}$

Step 7

Combine the numerators over the common denominator.

$\frac{3 x^{2} - (6 x^{2} - 5)}{3 x^{2}}$

Step 8

Rewrite $\frac{3 x^{2} - (6 x^{2} - 5)}{3 x^{2}}$ in a factored form.

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Step 8.1

Apply the distributive property.

$\frac{3 x^{2} - (6 x^{2}) - - 5}{3 x^{2}}$

Step 8.2

Multiply $6$ by $- 1$ .

$\frac{3 x^{2} - 6 x^{2} - - 5}{3 x^{2}}$

Step 8.3

Multiply $- 1$ by $- 5$ .

$\frac{3 x^{2} - 6 x^{2} + 5}{3 x^{2}}$

Step 8.4

Subtract $6 x^{2}$ from $3 x^{2}$ .

$\frac{- 3 x^{2} + 5}{3 x^{2}}$