Solve f(x)=5/sqrt{3-x}

$$f ( x ) = \frac { 5 } { \sqrt { 3 } - x }$$

Evaluate

$$\frac{5}{-x+\sqrt{3}}$$

Short Solution Steps

Rationalize the denominator of \frac{5}{\sqrt{3}-x} by multiplying numerator and denominator by \sqrt{3}+x.

$$\frac{5\left(\sqrt{3}+x\right)}{\left(\sqrt{3}-x\right)\left(\sqrt{3}+x\right)}$$

Consider \left(\sqrt{3}-x\right)\left(\sqrt{3}+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{5\left(\sqrt{3}+x\right)}{\left(\sqrt{3}\right)^{2}-x^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5\left(\sqrt{3}+x\right)}{3-x^{2}}$$

Use the distributive property to multiply 5 by \sqrt{3}+x.

$$\frac{5\sqrt{3}+5x}{3-x^{2}}$$

Differentiate w.r.t. x

$$\frac{5}{\left(-x+\sqrt{3}\right)^{2}}$$