What is join (ydx+xdy)/(1-x^2y^2)+xdx ?

The solution to join (ydx+xdy)/(1-x^2y^2)+xdx is (ydx+xdy+xdx(1-y^2x^2))/(1-y^2x^2)

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join (ydx+xdy)/(1-x^2y^2)+xdx

join

\frac{y d x + x d y}{1 - x ^{2} y ^{2}} + x d x

\frac{y d x + x d y + x d x ( 1 - y ^{2} x ^{2} )}{1 - y ^{2} x ^{2}}

Solution steps

\frac{y d x + x d y}{1 - x ^{2} y ^{2}} + x d x

Convert element to fraction:

x d x = \frac{x d x ( 1 - x ^{2} y ^{2} )}{1 - x ^{2} y ^{2}}

= \frac{y d x + x d y}{1 - x ^{2} y ^{2}} + \frac{x d x ( 1 - x ^{2} y ^{2} )}{1 - x ^{2} y ^{2}}

Since the denominators are equal, combine the fractions:

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

= \frac{y d x + x d y + x d x ( 1 - x ^{2} y ^{2} )}{1 - x ^{2} y ^{2}}

w^{2} - 40 = 3 w

\frac{x}{4} + 1 = \frac{x}{2}

1 - (2 y - 3)^{2}

12 ab - 8 a

(x - 3)^{2} (x + 3)^{2}

What is join (ydx+xdy)/(1-x^2y^2)+xdx ?
The solution to join (ydx+xdy)/(1-x^2y^2)+xdx is (ydx+xdy+xdx(1-y^2x^2))/(1-y^2x^2)