Precalculus Examples

$f (x) = \frac{7}{x}$ , $g (x) = \frac{7}{x^{2}}$ , $(\frac{f}{g}) (x)$

Step 1

Evaluate $\frac{f}{g}$ .

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Step 1.1

Replace the function designators in $\frac{f}{g}$ with the actual functions.

$\frac{\frac{7}{x}}{\frac{7}{x^{2}}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{x} \cdot \frac{x^{2}}{7}$

Step 1.3

Combine.

$\frac{7 x^{2}}{x \cdot 7}$

Step 1.4

Cancel the common factor of $7$ .

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Step 1.4.1

Cancel the common factor.

$\frac{7 x^{2}}{x \cdot 7}$

Step 1.4.2

Rewrite the expression.

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

Step 1.5

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

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Step 1.5.1

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

$\frac{x \cdot x}{x}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

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

$\frac{x \cdot x}{x^{1}}$

Step 1.5.2.2

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

$\frac{x \cdot x}{x \cdot 1}$

Step 1.5.2.3

Cancel the common factor.

$\frac{x \cdot x}{x \cdot 1}$

Step 1.5.2.4

Rewrite the expression.

$\frac{x}{1}$

Step 1.5.2.5

Divide $x$ by $1$ .

$x$

Step 2

Evaluate $\frac{f}{g}$ at $x$ .

$x$

Step 3

Remove parentheses.

$x$