Question

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

Answer 1

Найдем общий знаменатель двух дробей (разность) : 2ху, значит к 1 дроби доп. множитель 2у, а ко второй х, в числителе получится. 4у^2-х^2 (формула) (2у-х)(2у+х)

(2у-х)(2у+х)/2ху * (на обратную дробь) 1/2у+х. сокращаем 2у+х, получится 2у-х/2ху, подставим теперь
2*1/2-1/9/2*1/2*1/9= 1-1/9/1/9=8/9/1/9 (умножаем на обратную) = 8 (при сокращении девяток)

Answer 2

To solve the expression (2y/x)-(x/2y):(2y+x) when x=1/9 and y=1/2, we need to substitute the given values into the expression and simplify using the order of operations (PEMDAS).

First, let's substitute the values of x and y into the expression:

(2(1/2)/(1/9)) - ((1/9)/(2(1/2))) : (2(1/2) + 1/9)

Next, we need to simplify using the order of operations. We start with the parentheses, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

(2(1/2)/(1/9)) - ((1/9)/(2(1/2))) : (2(1/2) + 1/9) = (1/2)/(1/9) - (1/9)/(2(1/2)) : (5/2 + 1/9) // Simplify the parentheses in the denominator = (1/2)/(1/9) - (1/9)/(2(1/2)) : (45/18 + 2/18) // Convert the denominator of the fraction in the denominator to a common denominator = (1/2)/(1/9) - (1/9)/(3) : (49/18) // Simplify 2(1/2) to 5/2 and add the fractions in the denominator = (9/2)/(1) - (3/9) : (49/18) // Divide by a fraction by dividing by its reciprocal = 9/2 - 1/3 : 49/18 // Simplify the division of the fractions in the denominator = (27/6) - (2/6) : (49/18) // Convert the fractions to have a common denominator = 25/6 : (49/18) // Subtract the numerators = (25/6) * (18/49) // Invert the divisor and multiply = 75/49

Therefore, the value of the expression is 75/49 when x=1/9 and y=1/2.