How to solve (1)/(sqrt(3)-3)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (1)/(sqrt(3)-3) | Equatix

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Question

$$\frac{ 1 }{ \sqrt{ 3 } -3 }$$

Evaluate

$-\frac{\sqrt{3}}{6}-\frac{1}{2}\approx -0.788675135$

Solution Steps

Rationalize the denominator of $\frac{1}{\sqrt{3}-3}$ by multiplying numerator and denominator by $\sqrt{3}+3$.

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

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

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

Square $\sqrt{3}$. Square $3$.

$$\frac{\sqrt{3}+3}{3-9}$$

Subtract $9$ from $3$ to get $-6$.

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

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