Algebra Examples

$\frac{5 x^{2}}{2} - \frac{2}{x}$

Step 1

To write $\frac{5 x^{2}}{2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5 x^{2}}{2} \cdot \frac{x}{x} - \frac{2}{x}$

Step 2

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

$\frac{5 x^{2}}{2} \cdot \frac{x}{x} - \frac{2}{x} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $2 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 x^{2}}{2}$ by $\frac{x}{x}$ .

$\frac{5 x^{2} x}{2 x} - \frac{2}{x} \cdot \frac{2}{2}$

Step 3.2

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

$\frac{5 x^{2} x}{2 x} - \frac{2 \cdot 2}{x \cdot 2}$

Step 3.3

Reorder the factors of $x \cdot 2$ .

$\frac{5 x^{2} x}{2 x} - \frac{2 \cdot 2}{2 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 x^{2} x - 2 \cdot 2}{2 x}$

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

Move $x$ .

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

Step 5.1.2

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

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Step 5.1.2.1

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

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

Step 5.1.2.2

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

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

Step 5.1.3

Add $1$ and $2$ .

$\frac{5 x^{3} - 2 \cdot 2}{2 x}$

Step 5.2

Multiply $- 2$ by $2$ .

$\frac{5 x^{3} - 4}{2 x}$