Solve c^2-23/c-sqrt{23}

$$\frac { c ^ { 2 } - 23 } { c - \sqrt { 23 } }$$

Evaluate

$$\frac{c^{2}-23}{c-\sqrt{23}}$$

Solution Steps

Rationalize the denominator of \frac{c^{2}-23}{c-\sqrt{23}} by multiplying numerator and denominator by c+\sqrt{23}.

$$\frac{\left(c^{2}-23\right)\left(c+\sqrt{23}\right)}{\left(c-\sqrt{23}\right)\left(c+\sqrt{23}\right)}$$

Consider \left(c-\sqrt{23}\right)\left(c+\sqrt{23}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(c^{2}-23\right)\left(c+\sqrt{23}\right)}{c^{2}-\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{\left(c^{2}-23\right)\left(c+\sqrt{23}\right)}{c^{2}-23}$$

Cancel out c^{2}-23 in both numerator and denominator.

$$c+\sqrt{23}$$

Differentiate w.r.t. c

$$1$$