What is expand (4(2x\frac{dy)/(dx)+y)}{xy} ?

The solution to expand (4(2x\frac{dy)/(dx)+y)}{xy} is (8(dy)/(dx))/y+4/x

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expand (4(2x\frac{dy)/(dx)+y)}{xy}

expand

\frac{4 ( 2 x \frac{d y}{d x} + y )}{x y}

\frac{8 \frac{d y}{d x}}{y} + \frac{4}{x}

Solution steps

\frac{4 ( 2 x \frac{d y}{d x} + y )}{x y}

Expand

4 (2 x \frac{d y}{d x} + y) : 8 x \frac{d y}{d x} + 4 y

= \frac{8 x \frac{d y}{d x} + 4 y}{x y}

Apply the fraction rule:

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

\frac{8 x \frac{d y}{d x} + 4 y}{x y} = \frac{8 x \frac{d y}{d x}}{x y} + \frac{4 y}{x y}

= \frac{8 x \frac{d y}{d x}}{x y} + \frac{4 y}{x y}

Cancel

\frac{8 x \frac{d y}{d x}}{x y} : \frac{8 \frac{d y}{d x}}{y}

= \frac{8 \frac{d y}{d x}}{y} + \frac{4 y}{x y}

Cancel

\frac{4 y}{x y} : \frac{4}{x}

= \frac{8 \frac{d y}{d x}}{y} + \frac{4}{x}

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What is expand (4(2x\frac{dy)/(dx)+y)}{xy} ?
The solution to expand (4(2x\frac{dy)/(dx)+y)}{xy} is (8(dy)/(dx))/y+4/x