How to solve * 3/(4 - 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 * 3/(4 - sqrt(7)) | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac { 3 } { 4 - \sqrt { 7 } }$$

Evaluate

$\frac{\sqrt{7}+4}{3}\approx 2.215250437$

Solution Steps

Rationalize the denominator of $\frac{3}{4-\sqrt{7}}$ by multiplying numerator and denominator by $4+\sqrt{7}$.

$$\frac{3\left(4+\sqrt{7}\right)}{\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)}$$

Consider $\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{3\left(4+\sqrt{7}\right)}{4^{2}-\left(\sqrt{7}\right)^{2}}$$

Square $4$. Square $\sqrt{7}$.

$$\frac{3\left(4+\sqrt{7}\right)}{16-7}$$

Subtract $7$ from $16$ to get $9$.

$$\frac{3\left(4+\sqrt{7}\right)}{9}$$

Divide $3\left(4+\sqrt{7}\right)$ by $9$ to get $\frac{1}{3}\left(4+\sqrt{7}\right)$.

$$\frac{1}{3}\left(4+\sqrt{7}\right)$$

Use the distributive property to multiply $\frac{1}{3}$ by $4+\sqrt{7}$.

$$\frac{1}{3}\times 4+\frac{1}{3}\sqrt{7}$$

Multiply $\frac{1}{3}$ and $4$ to get $\frac{4}{3}$.

$$\frac{4}{3}+\frac{1}{3}\sqrt{7}$$

Show Solution