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

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

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

simplify

\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}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

= \frac{y ^{3} x ^{2} - x ^{2} y ^{3}}{x y ( y ^{2} + x y ) ( x ^{2} + x y )}

Cancel

\frac{y ^{3} x ^{2} - x ^{2} y ^{3}}{x y ( y ^{2} + x y ) ( x ^{2} + x y )} : 0

= 0

i^{204}

(csc (x) - 1) (csc (x) + 1)

\frac{8}{3}

\frac{b - 8}{b ^{2} - b - 6} - \frac{1}{3 - b}

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