Question

$\frac{22}{2\sqrt{3}+1}+\frac{17}{2\sqrt{3}-1}$ is equal to $\frac{78\sqrt{3}-5}{m}$
then the value of m if m is rational number

Answer 1

$Werationalizethedenominators$

with the respective factors

$\frac{22}{2\sqrt{3}+1}\times \frac{2\sqrt{3}-1}{2\sqrt{3}-1}+\frac{17}{2\sqrt{3}-1}\times \frac{2\sqrt{3}+1}{2\sqrt{3}+1}$

$=\frac{44\sqrt{3}-22+34\sqrt{3}+17}{4\ast 3-1}=\frac{78\sqrt{3}-5}{11}$