Basic Math Examples

$\frac{8}{d - 2} - \frac{1}{{(d - 2)}^{2}}$

Step 1

To write $\frac{8}{d - 2}$ as a fraction with a common denominator, multiply by $\frac{d - 2}{d - 2}$ .

$\frac{8}{d - 2} \cdot \frac{d - 2}{d - 2} - \frac{1}{{(d - 2)}^{2}}$

Step 2

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

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Step 2.1

Multiply $\frac{8}{d - 2}$ by $\frac{d - 2}{d - 2}$ .

$\frac{8 (d - 2)}{(d - 2) (d - 2)} - \frac{1}{{(d - 2)}^{2}}$

Step 2.2

Raise $d - 2$ to the power of $1$ .

$\frac{8 (d - 2)}{{(d - 2)}^{1} (d - 2)} - \frac{1}{{(d - 2)}^{2}}$

Step 2.3

Raise $d - 2$ to the power of $1$ .

$\frac{8 (d - 2)}{{(d - 2)}^{1} {(d - 2)}^{1}} - \frac{1}{{(d - 2)}^{2}}$

Step 2.4

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

$\frac{8 (d - 2)}{{(d - 2)}^{1 + 1}} - \frac{1}{{(d - 2)}^{2}}$

Step 2.5

Add $1$ and $1$ .

$\frac{8 (d - 2)}{{(d - 2)}^{2}} - \frac{1}{{(d - 2)}^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{8 (d - 2) - 1}{{(d - 2)}^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{8 d + 8 \cdot - 2 - 1}{{(d - 2)}^{2}}$

Step 4.2

Multiply $8$ by $- 2$ .

$\frac{8 d - 16 - 1}{{(d - 2)}^{2}}$

Step 4.3

Subtract $1$ from $- 16$ .

$\frac{8 d - 17}{{(d - 2)}^{2}}$