Solve 2/s-sqrt{2}=

$$\frac { 2 } { s - \sqrt { 2 } } =$$

Evaluate

$$\frac{2}{s-\sqrt{2}}$$

Short Solution Steps

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

$$\frac{2\left(s+\sqrt{2}\right)}{\left(s-\sqrt{2}\right)\left(s+\sqrt{2}\right)}$$

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

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

The square of \sqrt{2} is 2.

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

Use the distributive property to multiply 2 by s+\sqrt{2}.

$$\frac{2s+2\sqrt{2}}{s^{2}-2}$$

Differentiate w.r.t. s

$$-\frac{2}{\left(s-\sqrt{2}\right)^{2}}$$