Rationalize and simplify the expression x/((x^2+r^2)^(1/2))

 Exercise

$\frac{x}{\sqrt{x^2+r^2}}$

 

To rationalize the denominator of the fraction, we multiply the numerator and denominator by $\sqrt{x^2+r^2}$

$\frac{x}{\sqrt{x^2+r^2}}\frac{\sqrt{x^2+r^2}}{\sqrt{x^2+r^2}}$

 

Multiplying fractions $\frac{x}{\sqrt{x^2+r^2}} \times \frac{\sqrt{x^2+r^2}}{\sqrt{x^2+r^2}}$

$\frac{x\sqrt{x^2+r^2}}{\sqrt{x^2+r^2}\cdot \sqrt{x^2+r^2}}$

 

When multiplying two powers that have the same base ($\sqrt{x^2+r^2}$), you can add the exponents

$\frac{x\sqrt{x^2+r^2}}{\left(\sqrt{x^2+r^2}\right)^2}$

 

Cancel exponents $\frac{1}{2}$ and $2$

$\frac{x\sqrt{x^2+r^2}}{x^2+r^2}$

$\frac{x\sqrt{x^2+r^2}}{x^2+r^2}$

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