Simplify 4/(x-4)+16/((x-4)^2)

$\frac{4}{x - 4} + \frac{16}{{(x - 4)}^{2}}$

Step 1

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

$\frac{4}{x - 4} \cdot \frac{x - 4}{x - 4} + \frac{16}{{(x - 4)}^{2}}$

Step 2

Write each expression with a common denominator of ${(x - 4)}^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x - 4}$ by $\frac{x - 4}{x - 4}$ .

$\frac{4 (x - 4)}{(x - 4) (x - 4)} + \frac{16}{{(x - 4)}^{2}}$

Raise $x - 4$ to the power of $1$ .

$\frac{4 (x - 4)}{{(x - 4)}^{1} (x - 4)} + \frac{16}{{(x - 4)}^{2}}$

Raise $x - 4$ to the power of $1$ .

$\frac{4 (x - 4)}{{(x - 4)}^{1} {(x - 4)}^{1}} + \frac{16}{{(x - 4)}^{2}}$

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

$\frac{4 (x - 4)}{{(x - 4)}^{1 + 1}} + \frac{16}{{(x - 4)}^{2}}$

Add $1$ and $1$ .

$\frac{4 (x - 4)}{{(x - 4)}^{2}} + \frac{16}{{(x - 4)}^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{4 (x - 4) + 16}{{(x - 4)}^{2}}$

Step 4

Simplify the numerator.

Factor $4$ out of $4 (x - 4) + 16$ .

Factor $4$ out of $16$ .

$\frac{4 (x - 4) + 4 \cdot 4}{{(x - 4)}^{2}}$

Factor $4$ out of $4 (x - 4) + 4 \cdot 4$ .

$\frac{4 (x - 4 + 4)}{{(x - 4)}^{2}}$

Add $- 4$ and $4$ .

$\frac{4 (x + 0)}{{(x - 4)}^{2}}$

Add $x$ and $0$ .

$\frac{4 x}{{(x - 4)}^{2}}$