Basic Math Examples

$\frac{5 a - 1}{5 a^{4}} + \frac{4 a + 1}{25 a^{3}}$

Step 1

To write $\frac{5 a - 1}{5 a^{4}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 a - 1}{5 a^{4}} \cdot \frac{5}{5} + \frac{4 a + 1}{25 a^{3}}$

Step 2

To write $\frac{4 a + 1}{25 a^{3}}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{5 a - 1}{5 a^{4}} \cdot \frac{5}{5} + \frac{4 a + 1}{25 a^{3}} \cdot \frac{a}{a}$

Step 3

Write each expression with a common denominator of $25 a^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 a - 1}{5 a^{4}}$ by $\frac{5}{5}$ .

$\frac{(5 a - 1) \cdot 5}{5 a^{4} \cdot 5} + \frac{4 a + 1}{25 a^{3}} \cdot \frac{a}{a}$

Step 3.2

Multiply $5$ by $5$ .

$\frac{(5 a - 1) \cdot 5}{25 a^{4}} + \frac{4 a + 1}{25 a^{3}} \cdot \frac{a}{a}$

Step 3.3

Multiply $\frac{4 a + 1}{25 a^{3}}$ by $\frac{a}{a}$ .

$\frac{(5 a - 1) \cdot 5}{25 a^{4}} + \frac{(4 a + 1) a}{25 a^{3} a}$

Step 3.4

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

$\frac{(5 a - 1) \cdot 5}{25 a^{4}} + \frac{(4 a + 1) a}{25 (a^{1} a^{3})}$

Step 3.5

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

$\frac{(5 a - 1) \cdot 5}{25 a^{4}} + \frac{(4 a + 1) a}{25 a^{1 + 3}}$

Step 3.6

Add $1$ and $3$ .

$\frac{(5 a - 1) \cdot 5}{25 a^{4}} + \frac{(4 a + 1) a}{25 a^{4}}$

Step 4

Combine the numerators over the common denominator.

$\frac{(5 a - 1) \cdot 5 + (4 a + 1) a}{25 a^{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{5 a \cdot 5 - 1 \cdot 5 + (4 a + 1) a}{25 a^{4}}$

Step 5.2

Multiply $5$ by $5$ .

$\frac{25 a - 1 \cdot 5 + (4 a + 1) a}{25 a^{4}}$

Step 5.3

Multiply $- 1$ by $5$ .

$\frac{25 a - 5 + (4 a + 1) a}{25 a^{4}}$

Step 5.4

Apply the distributive property.

$\frac{25 a - 5 + 4 a \cdot a + 1 a}{25 a^{4}}$

Step 5.5

Multiply $a$ by $a$ by adding the exponents.

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Step 5.5.1

Move $a$ .

$\frac{25 a - 5 + 4 (a \cdot a) + 1 a}{25 a^{4}}$

Step 5.5.2

Multiply $a$ by $a$ .

$\frac{25 a - 5 + 4 a^{2} + 1 a}{25 a^{4}}$

Step 5.6

Multiply $a$ by $1$ .

$\frac{25 a - 5 + 4 a^{2} + a}{25 a^{4}}$

Step 5.7

Add $25 a$ and $a$ .

$\frac{26 a - 5 + 4 a^{2}}{25 a^{4}}$

Step 5.8

Reorder terms.

$\frac{4 a^{2} + 26 a - 5}{25 a^{4}}$