What is expand y'(x)+((1-x)y)/x ?

The solution to expand y'(x)+((1-x)y)/x is y'(x)+y/x-y

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expand y'(x)+((1-x)y)/x

expand

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

y' (x) + \frac{y}{x} - y

Solution steps

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

Expand

(1 - x) y : y - x y

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

Apply the fraction rule:

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

\frac{y - x y}{x} = \frac{y}{x} - \frac{x y}{x}

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

Cancel

\frac{x y}{x} : y

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

(y^{- 1})^{4}

- \frac{( 6 x - 5 )}{( 3 x ^{2} - 5 x + 7 ) ^{2}}

\frac{\partial}{\partial x} ((y) (x - y))

\frac{( e ^{- s} )}{s ( s ^{2} + 1 )}

(- 1 + 2 i)^{4}

What is expand y'(x)+((1-x)y)/x ?
The solution to expand y'(x)+((1-x)y)/x is y'(x)+y/x-y