Finite Math Examples

$f (\frac{5}{x}) = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h}$

Step 1

Multiply both sides by $h$ .

$f (\frac{5}{x}) h = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $f (\frac{5}{x}) h$ .

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Step 2.1.1.1

Combine $f$ and $\frac{5}{x}$ .

$\frac{f \cdot 5}{x} h = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$

Step 2.1.1.2

Move $5$ to the left of $f$ .

$\frac{5 \cdot f}{x} h = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$

Step 2.1.1.3

Combine $\frac{5 f}{x}$ and $h$ .

$\frac{5 f h}{x} = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$ .

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Step 2.2.1.1

Cancel the common factor of $h$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{5 f h}{x} = \frac{f (\frac{5}{x} + h) - f \frac{5}{x}}{h} h$

Step 2.2.1.1.2

Rewrite the expression.

$\frac{5 f h}{x} = f (\frac{5}{x} + h) - f \frac{5}{x}$

Step 2.2.1.2

Simplify each term.

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Step 2.2.1.2.1

Apply the distributive property.

$\frac{5 f h}{x} = f \frac{5}{x} + f h - f \frac{5}{x}$

Step 2.2.1.2.2

Combine $f$ and $\frac{5}{x}$ .

$\frac{5 f h}{x} = \frac{f \cdot 5}{x} + f h - f \frac{5}{x}$

Step 2.2.1.2.3

Move $5$ to the left of $f$ .

$\frac{5 f h}{x} = \frac{5 f}{x} + f h - f \frac{5}{x}$

Step 2.2.1.2.4

Combine $\frac{5}{x}$ and $f$ .

$\frac{5 f h}{x} = \frac{5 f}{x} + f h - \frac{5 f}{x}$

Step 2.2.1.3

Combine the opposite terms in $\frac{5 f}{x} + f h - \frac{5 f}{x}$ .

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Step 2.2.1.3.1

Subtract $\frac{5 f}{x}$ from $\frac{5 f}{x}$ .

$\frac{5 f h}{x} = f h + 0$

Step 2.2.1.3.2

Add $f h$ and $0$ .

$\frac{5 f h}{x} = f h$

Step 3

Solve for $x$ .

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Step 3.1

Find the LCD of the terms in the equation.

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Step 3.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 3.1.2

The LCM of one and any expression is the expression.

$x$

Step 3.2

Multiply each term in $\frac{5 f h}{x} = f h$ by $x$ to eliminate the fractions.

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Step 3.2.1

Multiply each term in $\frac{5 f h}{x} = f h$ by $x$ .

$\frac{5 f h}{x} x = f h x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $x$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 f h}{x} x = f h x$

Step 3.2.2.1.2

Rewrite the expression.

$5 f h = f h x$

Step 3.3

Solve the equation.

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Step 3.3.1

Rewrite the equation as $f h x = 5 f h$ .

$f h x = 5 f h$

Step 3.3.2

Divide each term in $f h x = 5 f h$ by $f h$ and simplify.

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Step 3.3.2.1

Divide each term in $f h x = 5 f h$ by $f h$ .

$\frac{f h x}{f h} = \frac{5 f h}{f h}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $f$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{f h x}{f h} = \frac{5 f h}{f h}$

Step 3.3.2.2.1.2

Rewrite the expression.

$\frac{h x}{h} = \frac{5 f h}{f h}$

Step 3.3.2.2.2

Cancel the common factor of $h$ .

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Step 3.3.2.2.2.1

Cancel the common factor.

$\frac{h x}{h} = \frac{5 f h}{f h}$

Step 3.3.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{5 f h}{f h}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Cancel the common factor of $f$ .

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Step 3.3.2.3.1.1

Cancel the common factor.

$x = \frac{5 f h}{f h}$

Step 3.3.2.3.1.2

Rewrite the expression.

$x = \frac{5 h}{h}$

Step 3.3.2.3.2

Cancel the common factor of $h$ .

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Step 3.3.2.3.2.1

Cancel the common factor.

$x = \frac{5 h}{h}$

Step 3.3.2.3.2.2

Divide $5$ by $1$ .

$x = 5$