Evaluate ((3-7)^2+11)/(|-2|+|-1|)

$\frac{{(3 - 7)}^{2} + 11}{| - 2 | + | - 1 |}$

Simplify the numerator.

Subtract $7$ from $3$ .

$\frac{{(- 4)}^{2} + 11}{| - 2 | + | - 1 |}$

Raise $- 4$ to the power of $2$ .

$\frac{16 + 11}{| - 2 | + | - 1 |}$

Add $16$ and $11$ .

$\frac{27}{| - 2 | + | - 1 |}$

Simplify the denominator.

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{27}{2 + | - 1 |}$

The absolute value is the distance between a number and zero. The distance between $- 1$ and $0$ is $1$ .

$\frac{27}{2 + 1}$

Add $2$ and $1$ .

$\frac{27}{3}$

Divide $27$ by $3$ .

$9$