Basic Math Examples

$10 + \frac{1}{\frac{y}{10 - \frac{1}{y}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$10 + 1 \frac{10 - \frac{1}{y}}{y}$

Step 1.2

Multiply $\frac{10 - \frac{1}{y}}{y}$ by $1$ .

$10 + \frac{10 - \frac{1}{y}}{y}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$10 + \frac{\frac{10 y}{y} - \frac{1}{y}}{y}$

Step 1.3.2

Combine the numerators over the common denominator.

$10 + \frac{\frac{10 y - 1}{y}}{y}$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$10 + \frac{10 y - 1}{y} \cdot \frac{1}{y}$

Step 1.5

Multiply $\frac{10 y - 1}{y} \cdot \frac{1}{y}$ .

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Step 1.5.1

Multiply $\frac{10 y - 1}{y}$ by $\frac{1}{y}$ .

$10 + \frac{10 y - 1}{y \cdot y}$

Step 1.5.2

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

$10 + \frac{10 y - 1}{y^{1} y}$

Step 1.5.3

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

$10 + \frac{10 y - 1}{y^{1} y^{1}}$

Step 1.5.4

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

$10 + \frac{10 y - 1}{y^{1 + 1}}$

Step 1.5.5

Add $1$ and $1$ .

$10 + \frac{10 y - 1}{y^{2}}$

Step 2

To write $10$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

$\frac{10 y^{2}}{y^{2}} + \frac{10 y - 1}{y^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{10 y^{2} + 10 y - 1}{y^{2}}$