What is expand x*(1/x+y/(x^2)-3y^2) ?

The solution to expand x*(1/x+y/(x^2)-3y^2) is 1+y/x-3xy^2

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expand x*(1/x+y/(x^2)-3y^2)

expand

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

1 + \frac{y}{x} - 3 x y^{2}

Solution steps

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

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

Simplify

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

= 1 + \frac{y}{x} - 3 x y^{2}

(1 + \frac{3}{3}) (1 - \frac{3}{3})

(1)^{3}

\frac{2 x ^{2} + 7}{x ( x ^{2} + 1 )}

sin (2 t) \cdot U (t - π)

What is expand x*(1/x+y/(x^2)-3y^2) ?
The solution to expand x*(1/x+y/(x^2)-3y^2) is 1+y/x-3xy^2