Finite Math Examples

$\frac{t + w}{t w^{2}} + \frac{3 t + w}{t^{2} w}$

Step 1

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

$\frac{t + w}{t w^{2}} \cdot \frac{t}{t} + \frac{3 t + w}{t^{2} w}$

Step 2

To write $\frac{3 t + w}{t^{2} w}$ as a fraction with a common denominator, multiply by $\frac{w}{w}$ .

$\frac{t + w}{t w^{2}} \cdot \frac{t}{t} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3

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

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Step 3.1

Multiply $\frac{t + w}{t w^{2}}$ by $\frac{t}{t}$ .

$\frac{(t + w) t}{t w^{2} t} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3.2

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

$\frac{(t + w) t}{t^{1} t w^{2}} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3.3

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

$\frac{(t + w) t}{t^{1} t^{1} w^{2}} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3.4

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

$\frac{(t + w) t}{t^{1 + 1} w^{2}} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3.5

Add $1$ and $1$ .

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{3 t + w}{t^{2} w} \cdot \frac{w}{w}$

Step 3.6

Multiply $\frac{3 t + w}{t^{2} w}$ by $\frac{w}{w}$ .

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{(3 t + w) w}{t^{2} w \cdot w}$

Step 3.7

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

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{(3 t + w) w}{t^{2} (w^{1} w)}$

Step 3.8

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

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{(3 t + w) w}{t^{2} (w^{1} w^{1})}$

Step 3.9

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

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{(3 t + w) w}{t^{2} w^{1 + 1}}$

Step 3.10

Add $1$ and $1$ .

$\frac{(t + w) t}{t^{2} w^{2}} + \frac{(3 t + w) w}{t^{2} w^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{(t + w) t + (3 t + w) w}{t^{2} w^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{t \cdot t + w t + (3 t + w) w}{t^{2} w^{2}}$

Step 5.2

Multiply $t$ by $t$ .

$\frac{t^{2} + w t + (3 t + w) w}{t^{2} w^{2}}$

Step 5.3

Apply the distributive property.

$\frac{t^{2} + w t + 3 t w + w \cdot w}{t^{2} w^{2}}$

Step 5.4

Multiply $w$ by $w$ .

$\frac{t^{2} + w t + 3 t w + w^{2}}{t^{2} w^{2}}$

Step 5.5

Add $w t$ and $3 t w$ .

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Step 5.5.1

Reorder $w$ and $t$ .

$\frac{t^{2} + t w + 3 t w + w^{2}}{t^{2} w^{2}}$

Step 5.5.2

Add $t w$ and $3 t w$ .

$\frac{t^{2} + 4 t w + w^{2}}{t^{2} w^{2}}$