Algebra Examples

$\frac{2 x}{y} - \frac{6}{3 x y}$

Step 1

Cancel the common factor of $6$ and $3$ .

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Step 1.1

Factor $3$ out of $6$ .

$\frac{2 x}{y} - \frac{3 \cdot 2}{3 x y}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3 x y$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

$\frac{2 x}{y} - \frac{2}{x y}$

Step 2

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

$\frac{2 x}{y} \cdot \frac{x}{x} - \frac{2}{x y}$

Step 3

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

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Step 3.1

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

$\frac{2 x \cdot x}{y x} - \frac{2}{x y}$

Step 3.2

Reorder the factors of $y x$ .

$\frac{2 x \cdot x}{x y} - \frac{2}{x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 x \cdot x - 2}{x y}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $2$ out of $2 x \cdot x - 2$ .

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Step 5.1.1

Factor $2$ out of $2 x \cdot x$ .

$\frac{2 (x \cdot x) - 2}{x y}$

Step 5.1.2

Factor $2$ out of $- 2$ .

$\frac{2 (x \cdot x) + 2 (- 1)}{x y}$

Step 5.1.3

Factor $2$ out of $2 (x \cdot x) + 2 (- 1)$ .

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

Add $1$ and $1$ .

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

Step 5.6

Rewrite $1$ as $1^{2}$ .

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

Step 5.7

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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