How to solve -(20)/(sqrt(3)-1)

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

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Question

$$- \frac{ 20 }{ \sqrt{ 3 } -1 }$$

Evaluate

$-10\sqrt{3}-10\approx -27.320508076$

Solution Steps

Rationalize the denominator of $\frac{20}{\sqrt{3}-1}$ by multiplying numerator and denominator by $\sqrt{3}+1$.

$$-\frac{20\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}$$

Consider $\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$-\frac{20\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}$$

Square $\sqrt{3}$. Square $1$.

$$-\frac{20\left(\sqrt{3}+1\right)}{3-1}$$

Subtract $1$ from $3$ to get $2$.

$$-\frac{20\left(\sqrt{3}+1\right)}{2}$$

Divide $20\left(\sqrt{3}+1\right)$ by $2$ to get $10\left(\sqrt{3}+1\right)$.

$$-10\left(\sqrt{3}+1\right)$$

Use the distributive property to multiply $10$ by $\sqrt{3}+1$.

$$-\left(10\sqrt{3}+10\right)$$

To find the opposite of $10\sqrt{3}+10$, find the opposite of each term.

$$-10\sqrt{3}-10$$

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