Question

(2y/x-x/2y):(2y+x) при x=1/9•y=1/6

Answer 1

Ответ:

6

Пошаговое объяснение:

$(\frac{2y}{x} -\frac{x}{2y} ): (2y+x) = \frac{4y^{2}-x^{2} }{2xy} *\frac{1}{2y+x} = \frac{(2y-x)(2y+x)}{2xy} *\frac{1}{2y+x} =\frac{2y-x}{2xy}$

$\frac{2*\frac{1}{6}-\frac{1}{9} }{2*\frac{1}{6}*\frac{1}{9} } = \frac{\frac{2}{9} }{\frac{1}{27} } =\frac{2}{9} : \frac{1}{27} = \frac{2}{9} *27= 2*3=6$

Answer 2

To evaluate the expression (2y/x - x/2y) / (2y + x) when x = 1/9 and y = 1/6, we can substitute the given values into the expression and simplify it step by step.

Let's start by substituting the values:

Expression = (2 * (1/6) / (1/9)) - ((1/9) / (2 * (1/6))) / (2 * (1/6) + (1/9))

Now, simplify each term:

Expression = (2/6 * 9/1) - (1/9 / 2/6) / (2/6 * 6/1 + 1/9) = (1/3 * 9) - (1/9 / 1/3) / (1/3 * 6 + 1/9) = 3 - (1/9 * 3/1) / (2/3 + 1/9) = 3 - (3/9) / (6/9 + 1/9) = 3 - (3/9) / (7/9) = 3 - (3/9) * (9/7) = 3 - 1/7 = 21/7 - 1/7 = 20/7 = 2.857 (approximately)

Therefore, when x = 1/9 and y = 1/6, the expression (2y/x - x/2y) / (2y + x) evaluates to approximately 2.857.