Solve 2x-x/sqrt{5-15}

$$\frac { 2 x - x } { \sqrt { 5 } - 15 }$$

Factor

$$-\frac{\left(\sqrt{5}+15\right)x}{220}$$

Solution Steps

Combine 2x and -x to get x.

$$factor(\frac{x}{\sqrt{5}-15})$$

Rationalize the denominator of \frac{x}{\sqrt{5}-15} by multiplying numerator and denominator by \sqrt{5}+15.

$$factor(\frac{x\left(\sqrt{5}+15\right)}{\left(\sqrt{5}-15\right)\left(\sqrt{5}+15\right)})$$

Consider \left(\sqrt{5}-15\right)\left(\sqrt{5}+15\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$factor(\frac{x\left(\sqrt{5}+15\right)}{\left(\sqrt{5}\right)^{2}-15^{2}})$$

Square \sqrt{5}. Square 15.

$$factor(\frac{x\left(\sqrt{5}+15\right)}{5-225})$$

Subtract 225 from 5 to get -220.

$$factor(\frac{x\left(\sqrt{5}+15\right)}{-220})$$

Use the distributive property to multiply x by \sqrt{5}+15.

$$factor(\frac{x\sqrt{5}+15x}{-220})$$

Consider x\sqrt{5}+15x. Factor out x.

$$x\left(\sqrt{5}+15\right)$$

Rewrite the complete factored expression.

$$-\frac{x\left(\sqrt{5}+15\right)}{220}$$

Evaluate

$$-\frac{\left(\sqrt{5}+15\right)x}{220}$$