Calculus Examples

$m (p q) = \frac{f (a + h) - f a}{h}$

Step 1

Divide each term in $m p q = \frac{f (a + h) - f a}{h}$ by $p q$ .

$\frac{m p q}{p q} = \frac{\frac{f (a + h) - f a}{h}}{p q}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $p$ .

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Step 2.1.1

Cancel the common factor.

$\frac{m p q}{p q} = \frac{\frac{f (a + h) - f a}{h}}{p q}$

Step 2.1.2

Rewrite the expression.

$\frac{m q}{q} = \frac{\frac{f (a + h) - f a}{h}}{p q}$

Step 2.2

Cancel the common factor of $q$ .

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Step 2.2.1

Cancel the common factor.

$\frac{m q}{q} = \frac{\frac{f (a + h) - f a}{h}}{p q}$

Step 2.2.2

Divide $m$ by $1$ .

$m = \frac{\frac{f (a + h) - f a}{h}}{p q}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{f (a + h) - f a}{h} \cdot \frac{1}{p q}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Factor $f$ out of $f (a + h) - f a$ .

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Step 3.2.1.1

Factor $f$ out of $- f a$ .

$m = \frac{f (a + h) + f (- 1 a)}{h} \cdot \frac{1}{p q}$

Step 3.2.1.2

Factor $f$ out of $f (a + h) + f (- 1 a)$ .

$m = \frac{f (a + h - 1 a)}{h} \cdot \frac{1}{p q}$

Step 3.2.2

Rewrite $- 1 a$ as $- a$ .

$m = \frac{f (a + h - a)}{h} \cdot \frac{1}{p q}$

Step 3.2.3

Subtract $a$ from $a$ .

$m = \frac{f (h + 0)}{h} \cdot \frac{1}{p q}$

Step 3.2.4

Add $h$ and $0$ .

$m = \frac{f h}{h} \cdot \frac{1}{p q}$

Step 3.3

Simplify terms.

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Step 3.3.1

Cancel the common factor of $h$ .

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Step 3.3.1.1

Cancel the common factor.

$m = \frac{f h}{h} \cdot \frac{1}{p q}$

Step 3.3.1.2

Divide $f$ by $1$ .

$m = f \frac{1}{p q}$

Step 3.3.2

Combine $f$ and $\frac{1}{p q}$ .

$m = \frac{f}{p q}$