Pre-Algebra Examples

$\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2}$

Step 1

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

$\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2} \cdot \frac{x^{2}}{x^{2}}$

Step 2

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

Tap for more steps...

Step 2.1

Multiply $\frac{x}{x - 2}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{(x - 2) x^{2}}$

Step 2.2

Reorder the factors of $(x - 2) x^{2}$ .

$\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{x^{2} (x - 2)}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 + x \cdot x^{2}}{x^{2} (x - 2)}$

Step 4

Multiply $x$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 4.1.1

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

$\frac{5 + x^{1} x^{2}}{x^{2} (x - 2)}$

Step 4.1.2

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

$\frac{5 + x^{1 + 2}}{x^{2} (x - 2)}$

Step 4.2

Add $1$ and $2$ .

$\frac{5 + x^{3}}{x^{2} (x - 2)}$