Solve x^2-10/x-sqrt{10}

$$\frac { x ^ { 2 } - 10 } { x - \sqrt { 10 } }$$

Evaluate

$$\frac{x^{2}-10}{x-\sqrt{10}}$$

Solution Steps

Rationalize the denominator of \frac{x^{2}-10}{x-\sqrt{10}} by multiplying numerator and denominator by x+\sqrt{10}.

$$\frac{\left(x^{2}-10\right)\left(x+\sqrt{10}\right)}{\left(x-\sqrt{10}\right)\left(x+\sqrt{10}\right)}$$

Consider \left(x-\sqrt{10}\right)\left(x+\sqrt{10}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(x^{2}-10\right)\left(x+\sqrt{10}\right)}{x^{2}-\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\left(x^{2}-10\right)\left(x+\sqrt{10}\right)}{x^{2}-10}$$

Cancel out x^{2}-10 in both numerator and denominator.

$$x+\sqrt{10}$$

Differentiate w.r.t. x

$$1$$