How to solve 1/(4 + 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/(4 + sqrt(3)) | Equatix

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Question

$$\frac{1}{4+\sqrt{3}}$$

Evaluate

$\frac{4-\sqrt{3}}{13}\approx 0.17445763$

Solution Steps

Rationalize the denominator of $\frac{1}{4+\sqrt{3}}$ by multiplying numerator and denominator by $4-\sqrt{3}$.

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

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

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

Square $4$. Square $\sqrt{3}$.

$$\frac{4-\sqrt{3}}{16-3}$$

Subtract $3$ from $16$ to get $13$.

$$\frac{4-\sqrt{3}}{13}$$

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