Questions: (left(x/(x+y)-(y/(2x-y))+(xy+y^2-y)/(2x^2+xy-y^2)right))

(left(x/(x+y)-(y/(2x-y))+(xy+y^2-y)/(2x^2+xy-y^2)right))
Transcript text: $\left(\frac{x}{x+y}-\frac{y}{2 x-y}+\frac{\left(x y+y^{2}-y\right)}{2 x^{2}+x y-y^{2}}\right)$
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Solution

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To simplify the given expression, we need to combine the fractions by finding a common denominator and then simplifying the resulting expression.

Paso 1: Definir la expresión original

La expresión original es: \[ \frac{x}{x+y} - \frac{y}{2x-y} + \frac{xy + y^2 - y}{2x^2 + xy - y^2} \]

Paso 2: Simplificar la expresión

Para simplificar la expresión, combinamos las fracciones encontrando un denominador común y simplificando el resultado. La expresión simplificada es: \[ \frac{2x^2 - xy - y}{2x^2 + xy - y^2} \]

Respuesta Final

\[ \boxed{\frac{2x^2 - xy - y}{2x^2 + xy - y^2}} \]

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