Bài 1
a) \(A=\left[\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{2}{a+b}.\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\right].\dfrac{ab}{\left(a+b\right)^2}\)
\(=\left(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{2}{a+b}.\dfrac{a+b}{ab}\right).\dfrac{ab}{\left(a+b\right)^2}\)
\(=\dfrac{b^2+a^2+2ab}{a^2b^2}.\dfrac{ab}{\left(a+b\right)^2}\)
\(=\dfrac{\left(a+b\right)^2.ab}{a^2b^2.\left(a+b\right)^2}\)
\(=\dfrac{1}{ab}\)
b) \(B=\left[\dfrac{1}{\left(2x-y\right)^2}+\dfrac{2}{4x^2-y^2}+\dfrac{1}{\left(2x+y\right)^2}\right].\dfrac{4x^2+4xy+y^2}{16x}\)
\(=\left[\dfrac{1}{\left(2x-y\right)^2}+\dfrac{2}{\left(2x-y\right)\left(2x+y\right)}+\dfrac{1}{\left(2x+y\right)^2}\right].\dfrac{\left(2x+y\right)^2}{16x}\)
\(=\dfrac{\left(2x+y\right)^2+2\left(2x-y\right)\left(2x+y\right)+\left(2x-y\right)^2}{\left(2x-y\right)^2\left(2x+y\right)^2}.\dfrac{\left(2x+y\right)^2}{16x}\)
\(=\dfrac{4x^2+4xy+y^2+8x^2-2y^2+4x^2-4xy+y^2}{\left(2x-y\right)^2\left(2x+y\right)^2}.\dfrac{\left(2x+y\right)^2}{16x}\)
\(=\dfrac{16x^2.\left(2x+y\right)^2}{\left(2x-y\right)^2\left(2x+y\right)^2.16x}\)
\(=\dfrac{x}{\left(2x-y\right)^2}\)
