Pre-Algebra Examples

$(f g) (x) = x^{2} - 4$

Step 1

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

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

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $g$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Divide $f$ by $1$ .

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

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

$f = \frac{x \cdot x}{g x} + \frac{- 4}{g x}$

Step 3.1.1.2

Cancel the common factors.

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Step 3.1.1.2.1

Factor $x$ out of $g x$ .

$f = \frac{x \cdot x}{x g} + \frac{- 4}{g x}$

Step 3.1.1.2.2

Cancel the common factor.

$f = \frac{x \cdot x}{x g} + \frac{- 4}{g x}$

Step 3.1.1.2.3

Rewrite the expression.

$f = \frac{x}{g} + \frac{- 4}{g x}$

Step 3.1.2

Move the negative in front of the fraction.

$f = \frac{x}{g} - \frac{4}{g x}$