How to solve 1/(sqrt(- 7) - 2)

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(- 7) - 2) | Equatix

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Question

$$\frac{1}{\sqrt{-7}-2}$$

Evaluate

$\text{Indeterminate}$

Solution Steps

Rationalize the denominator of $\frac{1}{\sqrt{-7}-2}$ by multiplying numerator and denominator by $\sqrt{-7}+2$.

$$\frac{\sqrt{-7}+2}{\left(\sqrt{-7}-2\right)\left(\sqrt{-7}+2\right)}$$

Consider $\left(\sqrt{-7}-2\right)\left(\sqrt{-7}+2\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{\sqrt{-7}+2}{\left(\sqrt{-7}\right)^{2}-2^{2}}$$

Square $\sqrt{-7}$. Square $2$.

$$\frac{\sqrt{-7}+2}{-7-4}$$

Subtract $4$ from $-7$ to get $-11$.

$$\frac{\sqrt{-7}+2}{-11}$$

Multiply both numerator and denominator by -1.

$$\frac{-\sqrt{-7}-2}{11}$$

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