Solve 2/sqrt{3-4}

$$\frac{ 2 }{ \sqrt{ 3 } -4 }$$

Evaluate

$$\frac{-2\sqrt{3}-8}{13}\approx -0.88185397$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{3}-4} by multiplying numerator and denominator by \sqrt{3}+4.

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

Consider \left(\sqrt{3}-4\right)\left(\sqrt{3}+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square \sqrt{3}. Square 4.

$$\frac{2\left(\sqrt{3}+4\right)}{3-16}$$

Subtract 16 from 3 to get -13.

$$\frac{2\left(\sqrt{3}+4\right)}{-13}$$

Use the distributive property to multiply 2 by \sqrt{3}+4.

$$\frac{2\sqrt{3}+8}{-13}$$