Evaluate Using the Given Value (3x+2y+z)/(x+y+z) , x=2 , y=3 , z=1

$\frac{3 x + 2 y + z}{x + y + z}$ , $x = 2$ , $y = 3$ , $z = 1$

Step 1

Replace the variable $x$ with $2$ in the expression.

$\frac{3 (2) + 2 y + z}{(2) + y + z}$

Step 2

Replace the variable $y$ with $3$ in the expression.

$\frac{3 (2) + 2 (3) + z}{2 + 3 + z}$

Step 3

Replace the variable $z$ with $1$ in the expression.

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

Step 4

Remove parentheses.

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

Step 5

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 + 2 (3) + 1}{2 + 3 + 1}$

Multiply $2$ by $3$ .

$\frac{6 + 6 + 1}{2 + 3 + 1}$

Add $6$ and $6$ .

$\frac{12 + 1}{2 + 3 + 1}$

Add $12$ and $1$ .

$\frac{13}{2 + 3 + 1}$

Step 6

Simplify the denominator.

Add $2$ and $3$ .

$\frac{13}{5 + 1}$

Add $5$ and $1$ .

$\frac{13}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{6}$

Decimal Form:

$2.1\overline{6}$

Mixed Number Form:

$2 \frac{1}{6}$