Algebra Examples

$\frac{x^{2} - 4}{x - 2} = 2 x - 1$

Step 1

Factor each term.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{x^{2} - 2^{2}}{x - 2} = 2 x - 1$

Step 1.2

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 $b = 2$ .

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

Step 1.3

Reduce the expression by cancelling the common factors.

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Step 1.3.1

Reduce the expression $\frac{(x + 2) (x - 2)}{x - 2}$ by cancelling the common factors.

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Step 1.3.1.1

Cancel the common factor.

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

Step 1.3.1.2

Rewrite the expression.

$\frac{x + 2}{1} = 2 x - 1$

Step 1.3.2

Divide $x + 2$ by $1$ .

$x + 2 = 2 x - 1$

Step 2

Solve the equation.

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Subtract $2 x$ from both sides of the equation.

$x + 2 - 2 x = - 1$

Step 2.1.2

Subtract $2 x$ from $x$ .

$- x + 2 = - 1$

Step 2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$- x = - 1 - 2$

Step 2.2.2

Subtract $2$ from $- 1$ .

$- x = - 3$

Step 2.3

Divide each term in $- x = - 3$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 3$ by $- 1$ .

$x = 3$