How to solve 1/(9 + 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 1/(9 + sqrt(6)) | Equatix

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Question

$$\frac{1}{9+\sqrt{6}}$$

Evaluate

$-\frac{\sqrt{6}}{75}+\frac{3}{25}\approx 0.087340137$

Solution Steps

Rationalize the denominator of $\frac{1}{9+\sqrt{6}}$ by multiplying numerator and denominator by $9-\sqrt{6}$.

$$\frac{9-\sqrt{6}}{\left(9+\sqrt{6}\right)\left(9-\sqrt{6}\right)}$$

Consider $\left(9+\sqrt{6}\right)\left(9-\sqrt{6}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{9-\sqrt{6}}{9^{2}-\left(\sqrt{6}\right)^{2}}$$

Square $9$. Square $\sqrt{6}$.

$$\frac{9-\sqrt{6}}{81-6}$$

Subtract $6$ from $81$ to get $75$.

$$\frac{9-\sqrt{6}}{75}$$

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