Solve (-3)div(-sqrt{5}-2)=

$$(-3) \div (- \sqrt{ 5 } -2)=$$

Evaluate

$$3\left(\sqrt{5}-2\right)\approx 0.708203932$$

Solution Steps

Rationalize the denominator of \frac{-3}{-\sqrt{5}-2} by multiplying numerator and denominator by -\sqrt{5}+2.

$$\frac{-3\left(-\sqrt{5}+2\right)}{\left(-\sqrt{5}-2\right)\left(-\sqrt{5}+2\right)}$$

Consider \left(-\sqrt{5}-2\right)\left(-\sqrt{5}+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-3\left(-\sqrt{5}+2\right)}{\left(-\sqrt{5}\right)^{2}-2^{2}}$$

Calculate -\sqrt{5} to the power of 2 and get \left(\sqrt{5}\right)^{2}.

$$\frac{-3\left(-\sqrt{5}+2\right)}{\left(\sqrt{5}\right)^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-3\left(-\sqrt{5}+2\right)}{\left(\sqrt{5}\right)^{2}-4}$$

The square of \sqrt{5} is 5.

$$\frac{-3\left(-\sqrt{5}+2\right)}{5-4}$$

Subtract 4 from 5 to get 1.

$$\frac{-3\left(-\sqrt{5}+2\right)}{1}$$

Anything divided by one gives itself.

$$-3\left(-\sqrt{5}+2\right)$$

Use the distributive property to multiply -3 by -\sqrt{5}+2.

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

Multiply -3 and -1 to get 3.

$$3\sqrt{5}-6$$