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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

100 (1 - \frac{1}{e ^{2}})

\frac{8 x ( x - 5 )}{4 x ^{2} - 27 x - 7}

8 (2 x + 3 y = 15)

3 - 3 \frac{3}{4}

(y + ey + e^{2} y)^{3}

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