Solve ((-11)+1)div(sqrt{8-11}-3)

$$((-11)+1) \div ( \sqrt{ 8-11 } -3)$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Add -11 and 1 to get -10.

$$\frac{-10}{\sqrt{8-11}-3}$$

Subtract 11 from 8 to get -3.

$$\frac{-10}{\sqrt{-3}-3}$$

Rationalize the denominator of \frac{-10}{\sqrt{-3}-3} by multiplying numerator and denominator by \sqrt{-3}+3.

$$\frac{-10\left(\sqrt{-3}+3\right)}{\left(\sqrt{-3}-3\right)\left(\sqrt{-3}+3\right)}$$

Consider \left(\sqrt{-3}-3\right)\left(\sqrt{-3}+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-10\left(\sqrt{-3}+3\right)}{\left(\sqrt{-3}\right)^{2}-3^{2}}$$

Square \sqrt{-3}. Square 3.

$$\frac{-10\left(\sqrt{-3}+3\right)}{-3-9}$$

Subtract 9 from -3 to get -12.

$$\frac{-10\left(\sqrt{-3}+3\right)}{-12}$$

Divide -10\left(\sqrt{-3}+3\right) by -12 to get \frac{5}{6}\left(\sqrt{-3}+3\right).

$$\frac{5}{6}\left(\sqrt{-3}+3\right)$$

Use the distributive property to multiply \frac{5}{6} by \sqrt{-3}+3.

$$\frac{5}{6}\sqrt{-3}+\frac{5}{6}\times 3$$

Express \frac{5}{6}\times 3 as a single fraction.

$$\frac{5}{6}\sqrt{-3}+\frac{5\times 3}{6}$$

Multiply 5 and 3 to get 15.

$$\frac{5}{6}\sqrt{-3}+\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{6}\sqrt{-3}+\frac{5}{2}$$