Linear Algebra Examples

$\frac{2}{4} + 1 = \frac{6}{2} n$

Step 1

Rewrite the equation as $\frac{6}{2} n = \frac{2}{4} + 1$ .

$\frac{6}{2} n = \frac{2}{4} + 1$

Step 2

Simplify.

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Step 2.1

Reduce the expression $\frac{6}{2}$ by cancelling the common factors.

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Step 2.1.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 3}{2} n = \frac{2}{4} + 1$

Step 2.1.2

Factor $2$ out of $2$ .

$\frac{2 \cdot 3}{2 (1)} n = \frac{2}{4} + 1$

Step 2.1.3

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 1} n = \frac{2}{4} + 1$

Step 2.1.4

Rewrite the expression.

$\frac{3}{1} n = \frac{2}{4} + 1$

Step 2.2

Divide $3$ by $1$ .

$3 n = \frac{2}{4} + 1$

Step 2.3

Reduce the expression $\frac{2}{4}$ by cancelling the common factors.

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Step 2.3.1

Factor $2$ out of $2$ .

$3 n = \frac{2 (1)}{4} + 1$

Step 2.3.2

Factor $2$ out of $4$ .

$3 n = \frac{2 \cdot 1}{2 \cdot 2} + 1$

Step 2.3.3

Cancel the common factor.

$3 n = \frac{2 \cdot 1}{2 \cdot 2} + 1$

Step 2.3.4

Rewrite the expression.

$3 n = \frac{1}{2} + 1$

Step 2.4

Write $1$ as a fraction with a common denominator.

$3 n = \frac{1}{2} + \frac{2}{2}$

Step 2.5

Combine the numerators over the common denominator.

$3 n = \frac{1 + 2}{2}$

Step 2.6

Add $1$ and $2$ .

$3 n = \frac{3}{2}$

Step 3

Divide each term in $3 n = \frac{3}{2}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 n = \frac{3}{2}$ by $3$ .

$\frac{3 n}{3} = \frac{\frac{3}{2}}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{\frac{3}{2}}{3}$

Step 3.2.1.2

Divide $n$ by $1$ .

$n = \frac{\frac{3}{2}}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$n = \frac{3}{2} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Cancel the common factor.

$n = \frac{3}{2} \cdot \frac{1}{3}$

Step 3.3.2.2

Rewrite the expression.

$n = \frac{1}{2}$

Step 4

The domain is the set of all valid $n$ values.

${n | n = \frac{1}{2}}$

Step 5