Algebra Examples

$\frac{3}{6 u} + \frac{3 u}{4 v}$

Step 1

Cancel the common factor of $3$ and $6$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{6 u} + \frac{3 u}{4 v}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $6 u$ .

$\frac{3 (1)}{3 (2 u)} + \frac{3 u}{4 v}$

Step 1.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 (2 u)} + \frac{3 u}{4 v}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{2 u} + \frac{3 u}{4 v}$

Step 2

To write $\frac{1}{2 u}$ as a fraction with a common denominator, multiply by $\frac{2 v}{2 v}$ .

$\frac{1}{2 u} \cdot \frac{2 v}{2 v} + \frac{3 u}{4 v}$

Step 3

To write $\frac{3 u}{4 v}$ as a fraction with a common denominator, multiply by $\frac{u}{u}$ .

$\frac{1}{2 u} \cdot \frac{2 v}{2 v} + \frac{3 u}{4 v} \cdot \frac{u}{u}$

Step 4

Write each expression with a common denominator of $4 u v$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2 u}$ by $\frac{2 v}{2 v}$ .

$\frac{2 v}{2 u (2 v)} + \frac{3 u}{4 v} \cdot \frac{u}{u}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{2 v}{4 u v} + \frac{3 u}{4 v} \cdot \frac{u}{u}$

Step 4.3

Multiply $\frac{3 u}{4 v}$ by $\frac{u}{u}$ .

$\frac{2 v}{4 u v} + \frac{3 u \cdot u}{4 v u}$

Step 4.4

Reorder the factors of $4 v u$ .

$\frac{2 v}{4 u v} + \frac{3 u \cdot u}{4 u v}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 v + 3 u \cdot u}{4 u v}$

Step 6

Multiply $u$ by $u$ by adding the exponents.

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Step 6.1

Move $u$ .

$\frac{2 v + 3 (u \cdot u)}{4 u v}$

Step 6.2

Multiply $u$ by $u$ .

$\frac{2 v + 3 u^{2}}{4 u v}$