How to solve (1)/(3-sqrt(7))

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)/(3-sqrt(7)) | Equatix

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Question

$$\frac{ 1 }{ 3- \sqrt{ 7 } }$$

Evaluate

$\frac{\sqrt{7}+3}{2}\approx 2.822875656$

Solution Steps

Rationalize the denominator of $\frac{1}{3-\sqrt{7}}$ by multiplying numerator and denominator by $3+\sqrt{7}$.

$$\frac{3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}$$

Consider $\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{3+\sqrt{7}}{3^{2}-\left(\sqrt{7}\right)^{2}}$$

Square $3$. Square $\sqrt{7}$.

$$\frac{3+\sqrt{7}}{9-7}$$

Subtract $7$ from $9$ to get $2$.

$$\frac{3+\sqrt{7}}{2}$$

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