Finite Math Examples

$a n = \frac{n}{n + 1}$

Step 1

Subtract $\frac{n}{n + 1}$ from both sides of the equation.

$a n - \frac{n}{n + 1} = 0$

Step 2

Simplify $a n - \frac{n}{n + 1}$ .

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Step 2.1

To write $a n$ as a fraction with a common denominator, multiply by $\frac{n + 1}{n + 1}$ .

$\frac{a n (n + 1)}{n + 1} - \frac{n}{n + 1} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{a n (n + 1) - n}{n + 1} = 0$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Factor $n$ out of $a n (n + 1) - n$ .

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Step 2.3.1.1

Factor $n$ out of $a n (n + 1)$ .

$\frac{n (a (n + 1)) - n}{n + 1} = 0$

Step 2.3.1.2

Factor $n$ out of $- n$ .

$\frac{n (a (n + 1)) + n \cdot - 1}{n + 1} = 0$

Step 2.3.1.3

Factor $n$ out of $n (a (n + 1)) + n \cdot - 1$ .

$\frac{n (a (n + 1) - 1)}{n + 1} = 0$

Step 2.3.2

Apply the distributive property.

$\frac{n (a n + a \cdot 1 - 1)}{n + 1} = 0$

Step 2.3.3

Multiply $a$ by $1$ .

$\frac{n (a n + a - 1)}{n + 1} = 0$

Step 3

Set the denominator in $\frac{n (a n + a - 1)}{n + 1}$ equal to $0$ to find where the expression is undefined.

$n + 1 = 0$

Step 4

Subtract $1$ from both sides of the equation.

$n = - 1$

Step 5