Algebra Examples

$\frac{1}{14} n + \frac{6}{17} n = - 4 + 4$

Step 1

Simplify $\frac{1}{14} n + \frac{6}{17} n$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{14}$ and $n$ .

$\frac{n}{14} + \frac{6}{17} n = - 4 + 4$

Step 1.1.2

Combine $\frac{6}{17}$ and $n$ .

$\frac{n}{14} + \frac{6 n}{17} = - 4 + 4$

Step 1.2

To write $\frac{n}{14}$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$\frac{n}{14} \cdot \frac{17}{17} + \frac{6 n}{17} = - 4 + 4$

Step 1.3

To write $\frac{6 n}{17}$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$\frac{n}{14} \cdot \frac{17}{17} + \frac{6 n}{17} \cdot \frac{14}{14} = - 4 + 4$

Step 1.4

Write each expression with a common denominator of $238$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{n}{14}$ by $\frac{17}{17}$ .

$\frac{n \cdot 17}{14 \cdot 17} + \frac{6 n}{17} \cdot \frac{14}{14} = - 4 + 4$

Step 1.4.2

Multiply $14$ by $17$ .

$\frac{n \cdot 17}{238} + \frac{6 n}{17} \cdot \frac{14}{14} = - 4 + 4$

Step 1.4.3

Multiply $\frac{6 n}{17}$ by $\frac{14}{14}$ .

$\frac{n \cdot 17}{238} + \frac{6 n \cdot 14}{17 \cdot 14} = - 4 + 4$

Step 1.4.4

Multiply $17$ by $14$ .

$\frac{n \cdot 17}{238} + \frac{6 n \cdot 14}{238} = - 4 + 4$

Step 1.5

Combine the numerators over the common denominator.

$\frac{n \cdot 17 + 6 n \cdot 14}{238} = - 4 + 4$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $n$ out of $n \cdot 17 + 6 n \cdot 14$ .

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Step 1.6.1.1

Factor $n$ out of $n \cdot 17$ .

$\frac{n (17) + 6 n \cdot 14}{238} = - 4 + 4$

Step 1.6.1.2

Factor $n$ out of $6 n \cdot 14$ .

$\frac{n (17) + n (6 \cdot 14)}{238} = - 4 + 4$

Step 1.6.1.3

Factor $n$ out of $n (17) + n (6 \cdot 14)$ .

$\frac{n (17 + 6 \cdot 14)}{238} = - 4 + 4$

Step 1.6.2

Multiply $6$ by $14$ .

$\frac{n (17 + 84)}{238} = - 4 + 4$

Step 1.6.3

Add $17$ and $84$ .

$\frac{n \cdot 101}{238} = - 4 + 4$

Step 1.7

Move $101$ to the left of $n$ .

$\frac{101 n}{238} = - 4 + 4$

Step 2

Add $- 4$ and $4$ .

$\frac{101 n}{238} = 0$

Step 3

Set the numerator equal to zero.

$101 n = 0$

Step 4

Divide each term in $101 n = 0$ by $101$ and simplify.

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Step 4.1

Divide each term in $101 n = 0$ by $101$ .

$\frac{101 n}{101} = \frac{0}{101}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $101$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{101 n}{101} = \frac{0}{101}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{0}{101}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $101$ .

$n = 0$