Question

Упростите выражение
$( frac{ sqrt{x} +1}{ sqrt{x} -1} - frac{ sqrt{x} -1}{ sqrt{x} +1} + 4 sqrt{x} ) * ( sqrt{x} - frac{1}{sqrt{x} } )$

Answer 1

$( frac{sqrt{x}+1}{sqrt{x}-1} - frac{sqrt{x}-1}{sqrt{x}+1} +4sqrt{x})cdot (sqrt{x}-frac{1}{sqrt{x}})=\\= frac{(sqrt{x}+1)^2-(sqrt{x}-1)^2+4sqrt{x}(x-1)}{x-1} cdot frac{x-1}{sqrt{x}} =\\= frac{4sqrt{x}+4xsqrt{x}-4sqrt{x}}{x-1} cdot frac{x-1}{sqrt{x}} = frac{4xsqrt{x}}{sqrt{x}} =4x$