Calculus Examples

$- \frac{6}{d^{2}} + \frac{c}{d}$

Step 1

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

$- \frac{6}{d^{2}} + \frac{c}{d} \cdot \frac{d}{d}$

Step 2

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

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Step 2.1

Multiply $\frac{c}{d}$ by $\frac{d}{d}$ .

$- \frac{6}{d^{2}} + \frac{c d}{d \cdot d}$

Step 2.2

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

$- \frac{6}{d^{2}} + \frac{c d}{d^{1} d}$

Step 2.3

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

$- \frac{6}{d^{2}} + \frac{c d}{d^{1} d^{1}}$

Step 2.4

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

$- \frac{6}{d^{2}} + \frac{c d}{d^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$- \frac{6}{d^{2}} + \frac{c d}{d^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 6 + c d}{d^{2}}$

Step 4

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{- 1 (6) + c d}{d^{2}}$

Step 5

Factor $- 1$ out of $c d$ .

$\frac{- 1 (6) - (- c d)}{d^{2}}$

Step 6

Factor $- 1$ out of $- 1 (6) - (- c d)$ .

$\frac{- 1 (6 - c d)}{d^{2}}$

Step 7

Move the negative in front of the fraction.

$- \frac{6 - c d}{d^{2}}$