What is expand ((x-2y)dx+(2x+y)dy)/x ?

The solution to expand ((x-2y)dx+(2x+y)dy)/x is dx-(2ydx)/x+2dy+(ydy)/x

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expand ((x-2y)dx+(2x+y)dy)/x

expand

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

d x - \frac{2 y d x}{x} + 2 d y + \frac{y d y}{x}

Solution steps

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

Expand

(x - 2 y) d x + (2 x + y) d y : x d x - 2 y d x + 2 x d y + y d y

= \frac{x d x - 2 y d x + 2 x d y + y d y}{x}

Apply the fraction rule:

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

\frac{x d x - 2 y d x + 2 x d y + y d y}{x} = \frac{x d x}{x} - \frac{2 y d x}{x} + \frac{2 x d y}{x} + \frac{y d y}{x}

= \frac{x d x}{x} - \frac{2 y d x}{x} + \frac{2 x d y}{x} + \frac{y d y}{x}

Cancel

\frac{x d x}{x} : d x

= d x - \frac{2 y d x}{x} + \frac{2 x d y}{x} + \frac{y d y}{x}

Cancel

\frac{2 x d y}{x} : 2 d y

= d x - \frac{2 y d x}{x} + 2 d y + \frac{y d y}{x}

x (- 1, 3) y (3, 0) z (- 1, - 2)

\frac{1}{( 7 + x ) ^{8}}

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

\frac{s + 3}{( s + 6 ) ^{2} ( s + 2 )}

10 (1 - e^{- 0.5 t})

What is expand ((x-2y)dx+(2x+y)dy)/x ?
The solution to expand ((x-2y)dx+(2x+y)dy)/x is dx-(2ydx)/x+2dy+(ydy)/x