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If x + 1/y = 2, then what is the value of {(x2y + 4xy + x)(2 – x)}/(2xy – x2y)?

If x + 1/y = 2, then what is the value of {(x2y + 4xy + x)(2 – x)}/(2xy – x2y)? Correct Answer 6

x + 1/y = 2

xy + 1 = 2y      ----(1)

= {(x2y + 4xy + x)(2 – x)} / (2xy – x2y)

= {x(xy + 4y + 1)(2 – x)} / {x(2y – xy)}

= {(xy + 4y + 1)(2 – x)} / {y(2 – x)}

= (xy + 4y + 1) /y

From equation (1):

= (2y + 4y) /y

= 6y/y

= 6

Smart trick

Put, x = y = 1

Hence, x + 1/y = 1 + 1 = 2 (satisfied)

Now, {(x2y + 4xy + x)(2 – x)}/(2xy – x2y)

= (1 + 4 + 1)(2 - 1)/(2 - 1)

= 6

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