Algebra Examples

$f (4 x) = \frac{x}{x^{2} + 1}$

Step 1

Remove parentheses.

$f \cdot 4 x = \frac{x}{x^{2} + 1}$

Step 2

Divide each term in $f \cdot (4 x) = \frac{x}{x^{2} + 1}$ by $4 x$ and simplify.

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Step 2.1

Divide each term in $f \cdot (4 x) = \frac{x}{x^{2} + 1}$ by $4 x$ .

$\frac{f \cdot (4 x)}{4 x} = \frac{\frac{x}{x^{2} + 1}}{4 x}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{f \cdot (4 x)}{4 x} = \frac{\frac{x}{x^{2} + 1}}{4 x}$

Step 2.2.1.2

Rewrite the expression.

$\frac{f \cdot (x)}{x} = \frac{\frac{x}{x^{2} + 1}}{4 x}$

Step 2.2.2

Cancel the common factor of $x$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{f \cdot x}{x} = \frac{\frac{x}{x^{2} + 1}}{4 x}$

Step 2.2.2.2

Divide $f$ by $1$ .

$f = \frac{\frac{x}{x^{2} + 1}}{4 x}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{4 x}$

Step 2.3.2

Cancel the common factor of $x$ .

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Step 2.3.2.1

Factor $x$ out of $4 x$ .

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{x \cdot 4}$

Step 2.3.2.2

Cancel the common factor.

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{x \cdot 4}$

Step 2.3.2.3

Rewrite the expression.

$f = \frac{1}{x^{2} + 1} \cdot \frac{1}{4}$

Step 2.3.3

Multiply $\frac{1}{x^{2} + 1}$ by $\frac{1}{4}$ .

$f = \frac{1}{(x^{2} + 1) \cdot 4}$

Step 2.3.4

Move $4$ to the left of $x^{2} + 1$ .

$f = \frac{1}{4 (x^{2} + 1)}$