\[\frac{1+\sqrt{7}}{2-\sqrt{7}}\]
1
Rationalize the denominator: 1+72−7⋅2+72+7=2+7+27+722−72\frac{1+\sqrt{7}}{2-\sqrt{7}} \cdot \frac{2+\sqrt{7}}{2+\sqrt{7}}=\frac{2+\sqrt{7}+2\sqrt{7}+7}{{2}^{2}-{\sqrt{7}}^{2}}.
2+7+27+722−72\frac{2+\sqrt{7}+2\sqrt{7}+7}{{2}^{2}-{\sqrt{7}}^{2}}

2
Collect like terms.
(2+7)+(7+27)22−72\frac{(2+7)+(\sqrt{7}+2\sqrt{7})}{{2}^{2}-{\sqrt{7}}^{2}}

3
Simplify  (2+7)+(7+27)(2+7)+(\sqrt{7}+2\sqrt{7})  to  9+379+3\sqrt{7}.
9+3722−72\frac{9+3\sqrt{7}}{{2}^{2}-{\sqrt{7}}^{2}}

4
Factor out the common term 33.
3(3+7)22−72\frac{3(3+\sqrt{7})}{{2}^{2}-{\sqrt{7}}^{2}}

5
Simplify  22{2}^{2}  to  44.
3(3+7)4−72\frac{3(3+\sqrt{7})}{4-{\sqrt{7}}^{2}}

6
Use this rule: x2=x{\sqrt{x}}^{2}=x.
3(3+7)4−7\frac{3(3+\sqrt{7})}{4-7}

7
Simplify  4−74-7  to  −3-3.
3(3+7)−3\frac{3(3+\sqrt{7})}{-3}

8
Move the negative sign to the left.
−3(3+7)3-\frac{3(3+\sqrt{7})}{3}

9
Cancel 33.
−(3+7)-(3+\sqrt{7})

10
Remove parentheses.
−3−7-3-\sqrt{7}

Done

Decimal Form: -5.645751
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