Question

Упростите выражение:
$(\frac{x^{\frac{1}{2} }+ x^{\frac{-1}{2} } }{2} )^{-2} * (\frac{x^{\frac{1}{2} } + 1 }{x^{\frac{1}{2} } - 1} + \frac{x^{\frac{1}{2} } - 1 }{x^{\frac{1}{2} } + 1})$

Answer 1

Ответ:

(8x)/(x²-1)

Объяснение:

((x^(1/2)+x^(-1/2))/2)⁻²·((x^(1/2)+1)/(x^(1/2)-1) +(x^(1/2)-1)/(x^(1/2)+1))=4/(√x +1/√x)² ·((√x +1)²+(√x -1)²)/((√x-1)(√x+1))=4/(x+2 +1/x) ·(x+2√x +1+x-2√x +1)/(x-1)=4/((x²+2x+1)/x) ·(2x+2)/(x-1)=(4x)/(x+1)² ·(2(x+1))/(x-1)=(8x)/((x+1)(x-1))=(8x)/(x²-1)