Question

Найдите значение выражения, если x=1/7, y=1/8

Answer 1

$x= \frac{1}{7}\; ,\; \; y= \frac{1}{8} \\\\(\frac{y}{x} - \frac{x}{y}):(x+y)= \frac{y^2-x^2}{xy}:(x+y)= \frac{(y-x)(y+x)}{xy} \cdot \frac{1}{x+y}=\\\\= \frac{y-x}{xy} = \frac{\frac{1}{8}-\frac{1}{7}}{\frac{1}{7}\cdot \frac{1}{8}} = \frac{-\frac{1}{56}}{\frac{1}{56}} =-1$

Answer 2

1)y/x-x/y=(y²-x²)/xy
2)(y-x)(y+x)/xy *1/(x+y)=(y-x)/xy
x=1/7,y=1/8
(1/8-1/7):(1/7*1/8)=(7-8)/56*56/1=-1