Algebra Examples

$m (x) = x^{2} - 4$

Step 1

Divide each term in $m x = x^{2} - 4$ by $x$ and simplify.

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Step 1.1

Divide each term in $m x = x^{2} - 4$ by $x$ .

$\frac{m x}{x} = \frac{x^{2}}{x} + \frac{- 4}{x}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $x$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{m x}{x} = \frac{x^{2}}{x} + \frac{- 4}{x}$

Step 1.2.1.2

Divide $m$ by $1$ .

$m = \frac{x^{2}}{x} + \frac{- 4}{x}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $x^{2}$ and $x$ .

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Step 1.3.1.1.1

Factor $x$ out of $x^{2}$ .

$m = \frac{x \cdot x}{x} + \frac{- 4}{x}$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

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

$m = \frac{x \cdot x}{x^{1}} + \frac{- 4}{x}$

Step 1.3.1.1.2.2

Factor $x$ out of $x^{1}$ .

$m = \frac{x \cdot x}{x \cdot 1} + \frac{- 4}{x}$

Step 1.3.1.1.2.3

Cancel the common factor.

$m = \frac{x \cdot x}{x \cdot 1} + \frac{- 4}{x}$

Step 1.3.1.1.2.4

Rewrite the expression.

$m = \frac{x}{1} + \frac{- 4}{x}$

Step 1.3.1.1.2.5

Divide $x$ by $1$ .

$m = x + \frac{- 4}{x}$

Step 1.3.1.2

Move the negative in front of the fraction.

$m = x - \frac{4}{x}$

Step 2

To rewrite as a function of $x$ , write the equation so that $m$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = x - \frac{4}{x}$