Mathematics

Mathematics

Problem

Evaluate the following difference and express the result in its simplest radical form. a. (i) Rationalise each denominator in the expression 34+3−34−3\displaystyle\frac{\sqrt{3}}{4+\sqrt{3}}-\frac{\sqrt{3}}{4-\sqrt{3}}. b. (ii) Simplify each fraction obtained in part (i) and hence find the exact value of the entire expression. c. (iii) Show that the final result is a rational number even though both original denominators were irrational.

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