What is expand (y(2x^{1/4}-xy^{1/3}+1))/(2x) ?

The solution to expand (y(2x^{1/4}-xy^{1/3}+1))/(2x) is y/(x^{3/4)}-(y^{4/3})/2+y/(2x)

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expand (y(2x^{1/4}-xy^{1/3}+1))/(2x)

expand

\frac{y ( 2 x ^{\frac{1}{4}} - x y ^{\frac{1}{3}} + 1 )}{2 x}

\frac{y}{x ^{\frac{3}{4}}} - \frac{y ^{\frac{4}{3}}}{2} + \frac{y}{2 x}

Solution steps

\frac{y ( 2 x ^{\frac{1}{4}} - x y ^{\frac{1}{3}} + 1 )}{2 x}

Expand

y (2 x^{\frac{1}{4}} - x y^{\frac{1}{3}} + 1) : 2 y x^{\frac{1}{4}} - x y^{\frac{4}{3}} + y

= \frac{2 y x ^{\frac{1}{4}} - x y ^{\frac{4}{3}} + y}{2 x}

Apply the fraction rule:

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

\frac{2 y x ^{\frac{1}{4}} - x y ^{\frac{4}{3}} + y}{2 x} = \frac{2 y x ^{\frac{1}{4}}}{2 x} - \frac{x y ^{\frac{4}{3}}}{2 x} + \frac{y}{2 x}

= \frac{2 y x ^{\frac{1}{4}}}{2 x} - \frac{x y ^{\frac{4}{3}}}{2 x} + \frac{y}{2 x}

Cancel

\frac{2 y x ^{\frac{1}{4}}}{2 x} : \frac{y}{x ^{\frac{3}{4}}}

= \frac{y}{x ^{\frac{3}{4}}} - \frac{x y ^{\frac{4}{3}}}{2 x} + \frac{y}{2 x}

Cancel

\frac{x y ^{\frac{4}{3}}}{2 x} : \frac{y ^{\frac{4}{3}}}{2}

= \frac{y}{x ^{\frac{3}{4}}} - \frac{y ^{\frac{4}{3}}}{2} + \frac{y}{2 x}

(x - 6)^{4}

10 (y + 5 x) e^{y + 5 x} + e^{y + 5 x} \cdot 5 (y + 5 x)^{2}

\frac{2 x}{( x - 1 ) ( x + 4 ) ( x ^{2} + 1 )}

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

\frac{1}{s ^{4} ( s - 5 )}

What is expand (y(2x^{1/4}-xy^{1/3}+1))/(2x) ?
The solution to expand (y(2x^{1/4}-xy^{1/3}+1))/(2x) is y/(x^{3/4)}-(y^{4/3})/2+y/(2x)