How to solve 1/(2 - sqrt(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/(2 - sqrt(3)) | Equatix

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Question

$$\frac{1}{2-\sqrt{3}}$$

Evaluate

$\sqrt{3}+2\approx 3.732050808$

Solution Steps

Rationalize the denominator of $\frac{1}{2-\sqrt{3}}$ by multiplying numerator and denominator by $2+\sqrt{3}$.

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

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

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

Square $2$. Square $\sqrt{3}$.

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

Subtract $3$ from $4$ to get $1$.

$$\frac{2+\sqrt{3}}{1}$$

Anything divided by one gives itself.

$$2+\sqrt{3}$$

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