Simplify (6x)/(x-3)+4/((x-3)^2)

$\frac{6 x}{x - 3} + \frac{4}{{(x - 3)}^{2}}$

Step 1

To write $\frac{6 x}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{6 x}{x - 3} \cdot \frac{x - 3}{x - 3} + \frac{4}{{(x - 3)}^{2}}$

Step 2

Write each expression with a common denominator of ${(x - 3)}^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 x}{x - 3}$ by $\frac{x - 3}{x - 3}$ .

$\frac{6 x (x - 3)}{(x - 3) (x - 3)} + \frac{4}{{(x - 3)}^{2}}$

Raise $x - 3$ to the power of $1$ .

$\frac{6 x (x - 3)}{{(x - 3)}^{1} (x - 3)} + \frac{4}{{(x - 3)}^{2}}$

Raise $x - 3$ to the power of $1$ .

$\frac{6 x (x - 3)}{{(x - 3)}^{1} {(x - 3)}^{1}} + \frac{4}{{(x - 3)}^{2}}$

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

$\frac{6 x (x - 3)}{{(x - 3)}^{1 + 1}} + \frac{4}{{(x - 3)}^{2}}$

Add $1$ and $1$ .

$\frac{6 x (x - 3)}{{(x - 3)}^{2}} + \frac{4}{{(x - 3)}^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 x (x - 3) + 4}{{(x - 3)}^{2}}$

Step 4

Simplify the numerator.

Factor $2$ out of $6 x (x - 3) + 4$ .

Factor $2$ out of $6 x (x - 3)$ .

$\frac{2 (3 x (x - 3)) + 4}{{(x - 3)}^{2}}$

Factor $2$ out of $4$ .

$\frac{2 (3 x (x - 3)) + 2 (2)}{{(x - 3)}^{2}}$

Factor $2$ out of $2 (3 x (x - 3)) + 2 (2)$ .

$\frac{2 (3 x (x - 3) + 2)}{{(x - 3)}^{2}}$

Apply the distributive property.

$\frac{2 (3 x \cdot x + 3 x \cdot - 3 + 2)}{{(x - 3)}^{2}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{2 (3 (x \cdot x) + 3 x \cdot - 3 + 2)}{{(x - 3)}^{2}}$

Multiply $x$ by $x$ .

$\frac{2 (3 x^{2} + 3 x \cdot - 3 + 2)}{{(x - 3)}^{2}}$

Multiply $- 3$ by $3$ .

$\frac{2 (3 x^{2} - 9 x + 2)}{{(x - 3)}^{2}}$