Linear Algebra Examples

$\frac{m - 2}{m + 1} + 2 \div 1 + \frac{1 + 2 m}{m + 1}$

Step 1

Combine the numerators over the common denominator.

$\frac{m - 2 + 1 + 2 m}{m + 1} + \frac{2}{1}$

Step 2

Add $m$ and $2 m$ .

$\frac{3 m - 2 + 1}{m + 1} + \frac{2}{1}$

Step 3

Simplify the expression.

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Step 3.1

Add $- 2$ and $1$ .

$\frac{3 m - 1}{m + 1} + \frac{2}{1}$

Step 3.2

Divide $2$ by $1$ .

$\frac{3 m - 1}{m + 1} + 2$

Step 4

To write $2$ as a fraction with a common denominator, multiply by $\frac{m + 1}{m + 1}$ .

$\frac{3 m - 1}{m + 1} + \frac{2 (m + 1)}{m + 1}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 m - 1 + 2 (m + 1)}{m + 1}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{3 m - 1 + 2 m + 2 \cdot 1}{m + 1}$

Step 6.2

Multiply $2$ by $1$ .

$\frac{3 m - 1 + 2 m + 2}{m + 1}$

Step 6.3

Add $3 m$ and $2 m$ .

$\frac{5 m - 1 + 2}{m + 1}$

Step 6.4

Add $- 1$ and $2$ .

$\frac{5 m + 1}{m + 1}$