What is (2xy-x/y)(xy^2+(2y)/x) ?

The solution to (2xy-x/y)(xy^2+(2y)/x) is (2y^2-1)(x^2y+2)

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simplify (2xy-x/y)(xy^2+(2y)/x)

simplify

(2 x y - \frac{x}{y}) (x y^{2} + \frac{2 y}{x})

(2 y^{2} - 1) (x^{2} y + 2)

Solution steps

(2 x y - \frac{x}{y}) (x y^{2} + \frac{2 y}{x})

Join

2 x y - \frac{x}{y} : \frac{2 x y ^{2} - x}{y}

= \frac{2 x y ^{2} - x}{y} (x y^{2} + \frac{2 y}{x})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 2 x y ^{2} - x ) ( x y ^{2} + \frac{2 y}{x} )}{y}

Simplify

(2 x y^{2} - x) (x y^{2} + \frac{2 y}{x}) : (2 y^{2} - 1) (x^{2} y^{2} + 2 y)

= \frac{( 2 y ^{2} - 1 ) ( x ^{2} y ^{2} + 2 y )}{y}

Factor

x^{2} y^{2} + 2 y : y (x^{2} y + 2)

= \frac{( 2 y ^{2} - 1 ) y ( x ^{2} y + 2 )}{y}

Cancel the common factor:

y

= (2 y^{2} - 1) (x^{2} y + 2)

x^{2} + 8 x + 7

\frac{1 ^{3}}{2}

x^{2} - 18 x + 32 = 0

x^{2} + 10 x = 39

1 - [\frac{- 5}{100} e^{- 5} - 0.01]

What is (2xy-x/y)(xy^2+(2y)/x) ?
The solution to (2xy-x/y)(xy^2+(2y)/x) is (2y^2-1)(x^2y+2)