Finite Math Examples

$h^{- 1} (5) = - 3$

Step 1

Add $3$ to both sides of the equation.

$h^{- 1} (5) + 3 = 0$

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{h} \cdot 5 + 3 = 0$

Step 2.2

Combine $\frac{1}{h}$ and $5$ .

$\frac{5}{h} + 3 = 0$

Step 3

To write $3$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

$\frac{5}{h} + \frac{3 h}{h} = 0$

Step 4

Combine the numerators over the common denominator.

$\frac{5 + 3 h}{h} = 0$

Step 5

Set the numerator equal to zero.

$5 + 3 h = 0$

Step 6

Solve the equation for $h$ .

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Step 6.1

Subtract $5$ from both sides of the equation.

$3 h = - 5$

Step 6.2

Divide each term in $3 h = - 5$ by $3$ and simplify.

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Step 6.2.1

Divide each term in $3 h = - 5$ by $3$ .

$\frac{3 h}{3} = \frac{- 5}{3}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $3$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{3 h}{3} = \frac{- 5}{3}$

Step 6.2.2.1.2

Divide $h$ by $1$ .

$h = \frac{- 5}{3}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Move the negative in front of the fraction.

$h = - \frac{5}{3}$