Algebra Examples

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

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 $1$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Factor $2$ out of $4$ .

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

Step 4.1.3

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

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

Step 4.2

Apply the distributive property.

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

Step 4.3

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

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Step 4.3.1

Move $x$ .

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

Step 4.3.2

Multiply $x$ by $x$ .

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

Step 4.4

Multiply $- 3$ by $3$ .

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