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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{2} = xx

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

Cancel the common factor:

x

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{2} = yy

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

Cancel the common factor:

y

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

(\frac{2 x - 1}{3 y})^{3}

9 m 12 + 23 n^{6} + 144

(a + b)^{3} - 8 (a - b)^{3}

- 1.7 (4 g - 9) - 3.6 g

- 3 - x

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