Question

-2%7D" id="TexFormula1" title="\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}" alt="\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}" align="absmiddle" class="latex-formula">
How do you simplify that expression?

Answer 1

Answer:

$\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}$

rationalise the denomimator:

$= \frac{ {x}^{ \frac{1}{4} } + 2 }{ {x}^{ \frac{1}{4} } - 2} . \frac{( {x}^{ \frac{1}{4} } + 2)}{ ({x}^{ \frac{1}{4} } + 2)} \\ \\ = \frac{ {x}^{ \frac{1}{2} } + 4 {x}^{ \frac{1}{4} } + 4 }{ {x}^{ \frac{1}{2} } - 4}$