Solve x^2-7/x-sqrt{7}=

$$\frac { x ^ { 2 } - 7 } { x - \sqrt { 7 } } =$$

Evaluate

$$\frac{x^{2}-7}{x-\sqrt{7}}$$

Solution Steps

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

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

Consider \left(x-\sqrt{7}\right)\left(x+\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}.

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

The square of \sqrt{7} is 7.

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

Cancel out x^{2}-7 in both numerator and denominator.

$$x+\sqrt{7}$$

Differentiate w.r.t. x

$$1$$