What is expand (3(y-x\frac{dy)/(dx))}{5y^2} ?

The solution to expand (3(y-x\frac{dy)/(dx))}{5y^2} is 3/(5y)-(3x\frac{dy)/(dx)}{5y^2}

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expand (3(y-x\frac{dy)/(dx))}{5y^2}

expand

\frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

\frac{3}{5 y} - \frac{3 x \frac{d y}{d x}}{5 y ^{2}}

Solution steps

\frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

Expand

3 (y - x \frac{d y}{d x}) : 3 y - 3 x \frac{d y}{d x}

= \frac{3 y - 3 x \frac{d y}{d x}}{5 y ^{2}}

Apply the fraction rule:

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

\frac{3 y - 3 x \frac{d y}{d x}}{5 y ^{2}} = \frac{3 y}{5 y ^{2}} - \frac{3 x \frac{d y}{d x}}{5 y ^{2}}

= \frac{3 y}{5 y ^{2}} - \frac{3 x \frac{d y}{d x}}{5 y ^{2}}

Cancel

\frac{3 y}{5 y ^{2}} : \frac{3}{5 y}

= \frac{3}{5 y} - \frac{3 x \frac{d y}{d x}}{5 y ^{2}}

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What is expand (3(y-x\frac{dy)/(dx))}{5y^2} ?
The solution to expand (3(y-x\frac{dy)/(dx))}{5y^2} is 3/(5y)-(3x\frac{dy)/(dx)}{5y^2}