How to solve (5)/(1-sqrt(6))

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 (5)/(1-sqrt(6)) | Equatix

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Question

$$\frac{ 5 }{ 1- \sqrt{ 6 } }$$

Evaluate

$-\sqrt{6}-1\approx -3.449489743$

Solution Steps

Rationalize the denominator of $\frac{5}{1-\sqrt{6}}$ by multiplying numerator and denominator by $1+\sqrt{6}$.

$$\frac{5\left(1+\sqrt{6}\right)}{\left(1-\sqrt{6}\right)\left(1+\sqrt{6}\right)}$$

Consider $\left(1-\sqrt{6}\right)\left(1+\sqrt{6}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{5\left(1+\sqrt{6}\right)}{1^{2}-\left(\sqrt{6}\right)^{2}}$$

Square $1$. Square $\sqrt{6}$.

$$\frac{5\left(1+\sqrt{6}\right)}{1-6}$$

Subtract $6$ from $1$ to get $-5$.

$$\frac{5\left(1+\sqrt{6}\right)}{-5}$$

Cancel out $-5$ and $-5$.

$$-\left(1+\sqrt{6}\right)$$

To find the opposite of $1+\sqrt{6}$, find the opposite of each term.

$$-1-\sqrt{6}$$

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