Question

(2y/x-x/2y):(2y+x) при x=1/9, y=1/6

Answer 1

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Answer 2

To solve this expression, we can start by substituting the given values of x and y:

(2y/x - x/2y) : (2y + x) = (2(1/6)/(1/9) - 1/9/(2(1/6))) : (2(1/6) + 1/9)

Simplifying the numerator:

2(1/6)/(1/9) - 1/9/(2(1/6)) = (13/6)/(1/9) - (1/9)/(13/6) [using the formula a/b ÷ c/d = ad/bc] = 13 * 6 / 1 - 1 / 13 * 6 / 1 [multiplying by reciprocal to simplify division] = (78 - 6) / 13 = 72 / 13

Simplifying the denominator:

2(1/6) + 1/9 = 13/6 + 1/9 [finding a common denominator] = (39 + 2) / 18 = 41 / 18

Now, substituting these values back into the original expression:

(72/13) : (41/18) = (72/13) * (18/41) [changing division to multiplication by reciprocal] = 72 * 18 / 13 * 41 = 1296 / 533

Therefore, the value of the expression is 1296/533 when x = 1/9 and y = 1/6.