Solve -4/3+sqrt{7}

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

Evaluate

$$2\left(\sqrt{7}-3\right)\approx -0.708497378$$

Solution Steps

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

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

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}.

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

Square 3. Square \sqrt{7}.

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

Subtract 7 from 9 to get 2.

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

Divide -4\left(3-\sqrt{7}\right) by 2 to get -2\left(3-\sqrt{7}\right).

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

Use the distributive property to multiply -2 by 3-\sqrt{7}.

$$-6+2\sqrt{7}$$