Question

Thực hiện phép tính sau:

\(\dfrac{x^2}{\left(x-y\right)^2\left(x+y\right)}-\dfrac{2x^2y^2}{x^4-2x^2y^2+y^4}+\dfrac{y^2}{\left(x^2-y^2\right)\left(x+y\right)}\)

Answer 1

MTC: \(\left(x-y\right)^2\left(x+y\right)^2\)

\(\dfrac{x^2}{\left(x-y\right)^2\left(x+y\right)}-\dfrac{2x^2y^2}{x^4-2x^2y^2+y^4}+\dfrac{y^2}{\left(x^2-y^2\right)\left(x+y\right)}\)

\(=\dfrac{x^2\left(x+y\right)-2xy^2+y^2\left(x-y\right)}{\left(x-y\right)^2\left(x+y\right)^2}\)

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

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

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

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

\(=\dfrac{1}{x-y}\)