Solve 5-a^2/sqrt{5-a}

$$\frac { 5 - a ^ { 2 } } { \sqrt { 5 } - a }$$

Evaluate

$$a+\sqrt{5}$$

Solution Steps

Rationalize the denominator of \frac{5-a^{2}}{\sqrt{5}-a} by multiplying numerator and denominator by \sqrt{5}+a.

$$\frac{\left(5-a^{2}\right)\left(\sqrt{5}+a\right)}{\left(\sqrt{5}-a\right)\left(\sqrt{5}+a\right)}$$

Consider \left(\sqrt{5}-a\right)\left(\sqrt{5}+a\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(5-a^{2}\right)\left(\sqrt{5}+a\right)}{\left(\sqrt{5}\right)^{2}-a^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\left(5-a^{2}\right)\left(\sqrt{5}+a\right)}{5-a^{2}}$$

Cancel out -a^{2}+5 in both numerator and denominator.

$$a+\sqrt{5}$$

Differentiate w.r.t. a

$$1$$