Solve 3/sqrt{6-3}

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

Evaluate

$$-\left(\sqrt{6}+3\right)\approx -5.449489743$$

Solution Steps

Rationalize the denominator of \frac{3}{\sqrt{6}-3} by multiplying numerator and denominator by \sqrt{6}+3.

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

Consider \left(\sqrt{6}-3\right)\left(\sqrt{6}+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}.

$$\frac{3\left(\sqrt{6}+3\right)}{\left(\sqrt{6}\right)^{2}-3^{2}}$$

Square \sqrt{6}. Square 3.

$$\frac{3\left(\sqrt{6}+3\right)}{6-9}$$

Subtract 9 from 6 to get -3.

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

Cancel out -3 and -3.

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

To find the opposite of \sqrt{6}+3, find the opposite of each term.

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