Question

Chứng minh đa thức nhau ko phụ thuộc vào biến

\(\dfrac{\left(x+y\right)^2}{x}.\left[\dfrac{x}{\left(x+y\right)^2}-\dfrac{x}{x^2-y^2}\right]-\dfrac{5x-3y}{y-x}\)

Answer 1

\(=\dfrac{\left(x+y\right)^2}{x}.\dfrac{x}{\left(x+y\right)^2}-\dfrac{\left(x+y\right)^2}{x}.\dfrac{x}{\left(x+y\right)\left(x-y\right)}-\dfrac{5x-3y}{y-x}\)

\(=1-\dfrac{x+y}{x-y}+\dfrac{5x-3y}{x-y}\)

\(=\dfrac{x-y-x-y+5x-3y}{x-y}=\dfrac{5x-5y}{x-y}=5\)