What is expand (x+y)/(xy)-(x+2y)/(xy+y^2)-y/(x^2+xy) ?

The solution to expand (x+y)/(xy)-(x+2y)/(xy+y^2)-y/(x^2+xy) is 0

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expand (x+y)/(xy)-(x+2y)/(xy+y^2)-y/(x^2+xy)

expand

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

0

Solution steps

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

Factor

y^{2} + x y : y (x + y)

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

Factor

x^{2} + x y : x (x + y)

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

Least Common Multiplier of

x y, y (x + y), x (x + y) : x y (x + y)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

x y (x + y) : x^{2} y + x y^{2}

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

Expand

(x + y)^{2} - (x + 2 y) x - y^{2} : 0

= \frac{0}{x ^{2} y + x y ^{2}}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

(1 + y cos (x)) d x - sin (x) d y

\frac{4 ( x + 2 ) ^{3}}{( s + 1 ) ( s - 1 ) ^{2}}

\frac{( 6 x - 1 ) ^{2}}{4}

(- 9 + 3) (4 - 7)

- 2 x^{\frac{7}{2}} (x^{2} + 1)

What is expand (x+y)/(xy)-(x+2y)/(xy+y^2)-y/(x^2+xy) ?
The solution to expand (x+y)/(xy)-(x+2y)/(xy+y^2)-y/(x^2+xy) is 0