Calculus Examples

$\frac{25}{\frac{a}{5 + a}} - a$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$25 \frac{5 + a}{a} - a$

Step 1.2

Combine $25$ and $\frac{5 + a}{a}$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Combine $- a$ and $\frac{a}{a}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{25 \cdot 5 + 25 a - a \cdot a}{a}$

Step 4.2

Multiply $25$ by $5$ .

$\frac{125 + 25 a - a \cdot a}{a}$

Step 4.3

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

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Step 4.3.1

Move $a$ .

$\frac{125 + 25 a - (a \cdot a)}{a}$

Step 4.3.2

Multiply $a$ by $a$ .

$\frac{125 + 25 a - a^{2}}{a}$