Question
Simplify :$\frac{22}{2 \sqrt{3}+1}+\frac{17}{2 \sqrt{3}-1}$
✓
Answer
$ \frac{22}{2 \sqrt{3}+1}+\frac{17}{2 \sqrt{3}-1}$
$ =\frac{22(2 \sqrt{3}-1)+17(2 \sqrt{3}+1)}{(2 \sqrt{3}+1)(2 \sqrt{3}-1)}$
$ =\frac{44 \sqrt{3}-22+34 \sqrt{3}+17}{(2 \sqrt{3})^2-1}$
$ =\frac{78 \sqrt{3}-5}{12-1}$
$ =\frac{78 \sqrt{3}-5}{11}$
$ =\frac{22(2 \sqrt{3}-1)+17(2 \sqrt{3}+1)}{(2 \sqrt{3}+1)(2 \sqrt{3}-1)}$
$ =\frac{44 \sqrt{3}-22+34 \sqrt{3}+17}{(2 \sqrt{3})^2-1}$
$ =\frac{78 \sqrt{3}-5}{12-1}$
$ =\frac{78 \sqrt{3}-5}{11}$
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