Algebra Examples

$\frac{3 - i}{4} - \frac{2 + i}{3}$

Step 1

Simplify each term.

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Step 1.1

Split the fraction $\frac{3 - i}{4}$ into two fractions.

$\frac{3}{4} + \frac{- i}{4} - \frac{2 + i}{3}$

Step 1.2

Move the negative in front of the fraction.

$\frac{3}{4} - \frac{i}{4} - \frac{2 + i}{3}$

Step 1.3

Split the fraction $\frac{2 + i}{3}$ into two fractions.

$\frac{3}{4} - \frac{i}{4} - (\frac{2}{3} + \frac{i}{3})$

Step 1.4

Apply the distributive property.

$\frac{3}{4} - \frac{i}{4} - \frac{2}{3} - \frac{i}{3}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{4} \cdot \frac{3}{3} - \frac{2}{3} - \frac{i}{4} - \frac{i}{3}$

Step 3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{4}{4} - \frac{i}{4} - \frac{i}{3}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{4 \cdot 3} - \frac{2}{3} \cdot \frac{4}{4} - \frac{i}{4} - \frac{i}{3}$

Step 4.2

Multiply $4$ by $3$ .

$\frac{3 \cdot 3}{12} - \frac{2}{3} \cdot \frac{4}{4} - \frac{i}{4} - \frac{i}{3}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 3}{12} - \frac{2 \cdot 4}{3 \cdot 4} - \frac{i}{4} - \frac{i}{3}$

Step 4.4

Multiply $3$ by $4$ .

$\frac{3 \cdot 3}{12} - \frac{2 \cdot 4}{12} - \frac{i}{4} - \frac{i}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 2 \cdot 4}{12} - \frac{i}{4} - \frac{i}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $3$ .

$\frac{9 - 2 \cdot 4}{12} - \frac{i}{4} - \frac{i}{3}$

Step 6.2

Multiply $- 2$ by $4$ .

$\frac{9 - 8}{12} - \frac{i}{4} - \frac{i}{3}$

Step 6.3

Subtract $8$ from $9$ .

$\frac{1}{12} - \frac{i}{4} - \frac{i}{3}$

Step 7

To write $- \frac{i}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{12} - \frac{i}{4} \cdot \frac{3}{3} - \frac{i}{3}$

Step 8

To write $- \frac{i}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{12} - \frac{i}{4} \cdot \frac{3}{3} - \frac{i}{3} \cdot \frac{4}{4}$

Step 9

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{i}{4}$ by $\frac{3}{3}$ .

$\frac{1}{12} - \frac{i \cdot 3}{4 \cdot 3} - \frac{i}{3} \cdot \frac{4}{4}$

Step 9.2

Multiply $4$ by $3$ .

$\frac{1}{12} - \frac{i \cdot 3}{12} - \frac{i}{3} \cdot \frac{4}{4}$

Step 9.3

Multiply $\frac{i}{3}$ by $\frac{4}{4}$ .

$\frac{1}{12} - \frac{i \cdot 3}{12} - \frac{i \cdot 4}{3 \cdot 4}$

Step 9.4

Multiply $3$ by $4$ .

$\frac{1}{12} - \frac{i \cdot 3}{12} - \frac{i \cdot 4}{12}$

Step 10

Combine the numerators over the common denominator.

$\frac{1}{12} + \frac{- 7 i}{12}$

Step 11

Move the negative in front of the fraction.

$\frac{1}{12} - \frac{7 i}{12}$