Finite Math Examples

$\frac{y + u}{y u^{2}} + \frac{4 y + u}{y^{2} u}$

Step 1

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

$\frac{y + u}{y u^{2}} \cdot \frac{y}{y} + \frac{4 y + u}{y^{2} u}$

Step 2

To write $\frac{4 y + u}{y^{2} u}$ as a fraction with a common denominator, multiply by $\frac{u}{u}$ .

$\frac{y + u}{y u^{2}} \cdot \frac{y}{y} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3

Write each expression with a common denominator of $y^{2} u^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{y + u}{y u^{2}}$ by $\frac{y}{y}$ .

$\frac{(y + u) y}{y u^{2} y} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3.2

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

$\frac{(y + u) y}{u^{2} (y^{1} y)} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3.3

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

$\frac{(y + u) y}{u^{2} (y^{1} y^{1})} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3.4

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

$\frac{(y + u) y}{u^{2} y^{1 + 1}} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3.5

Add $1$ and $1$ .

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{4 y + u}{y^{2} u} \cdot \frac{u}{u}$

Step 3.6

Multiply $\frac{4 y + u}{y^{2} u}$ by $\frac{u}{u}$ .

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{y^{2} u \cdot u}$

Step 3.7

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

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{y^{2} (u^{1} u)}$

Step 3.8

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

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{y^{2} (u^{1} u^{1})}$

Step 3.9

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

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{y^{2} u^{1 + 1}}$

Step 3.10

Add $1$ and $1$ .

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{y^{2} u^{2}}$

Step 3.11

Reorder the factors of $y^{2} u^{2}$ .

$\frac{(y + u) y}{u^{2} y^{2}} + \frac{(4 y + u) u}{u^{2} y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{(y + u) y + (4 y + u) u}{u^{2} y^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{y \cdot y + u y + (4 y + u) u}{u^{2} y^{2}}$

Step 5.2

Multiply $y$ by $y$ .

$\frac{y^{2} + u y + (4 y + u) u}{u^{2} y^{2}}$

Step 5.3

Apply the distributive property.

$\frac{y^{2} + u y + 4 y u + u \cdot u}{u^{2} y^{2}}$

Step 5.4

Multiply $u$ by $u$ .

$\frac{y^{2} + u y + 4 y u + u^{2}}{u^{2} y^{2}}$

Step 5.5

Add $u y$ and $4 y u$ .

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Step 5.5.1

Move $y$ .

$\frac{y^{2} + u y + 4 u y + u^{2}}{u^{2} y^{2}}$

Step 5.5.2

Add $u y$ and $4 u y$ .

$\frac{y^{2} + 5 u y + u^{2}}{u^{2} y^{2}}$