Basic Math Examples

$\frac{o}{k + y} = \frac{y^{2}}{k}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$o k = (k + y) y^{2}$

Step 2

Solve the equation for $k$ .

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Step 2.1

Simplify $(k + y) y^{2}$ .

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Step 2.1.1

Apply the distributive property.

$o k = k y^{2} + y \cdot y^{2}$

Step 2.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1.2.1

Multiply $y$ by $y^{2}$ .

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Step 2.1.2.1.1

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

$o k = k y^{2} + y^{1} y^{2}$

Step 2.1.2.1.2

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

$o k = k y^{2} + y^{1 + 2}$

Step 2.1.2.2

Add $1$ and $2$ .

$o k = k y^{2} + y^{3}$

Step 2.2

Subtract $k y^{2}$ from both sides of the equation.

$o k - k y^{2} = y^{3}$

Step 2.3

Factor $k$ out of $o k - k y^{2}$ .

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Step 2.3.1

Factor $k$ out of $o k$ .

$k o - k y^{2} = y^{3}$

Step 2.3.2

Factor $k$ out of $- k y^{2}$ .

$k o + k (- 1 y^{2}) = y^{3}$

Step 2.3.3

Factor $k$ out of $k o + k (- 1 y^{2})$ .

$k (o - 1 y^{2}) = y^{3}$

Step 2.4

Rewrite $- 1 y^{2}$ as $- y^{2}$ .

$k (o - y^{2}) = y^{3}$

Step 2.5

Divide each term in $k (o - y^{2}) = y^{3}$ by $o - y^{2}$ and simplify.

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Step 2.5.1

Divide each term in $k (o - y^{2}) = y^{3}$ by $o - y^{2}$ .

$\frac{k (o - y^{2})}{o - y^{2}} = \frac{y^{3}}{o - y^{2}}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $o - y^{2}$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{k (o - y^{2})}{o - y^{2}} = \frac{y^{3}}{o - y^{2}}$

Step 2.5.2.1.2

Divide $k$ by $1$ .

$k = \frac{y^{3}}{o - y^{2}}$