Question

Thực hiện phép tính :

a) 8/(x^2+3)*(x^2-1)+ 2/x^2+3+1/x

b) x+y/2*(x-y)-x-y/2(x+y)+2y^2/x^2-y^2

Answer 1

a: Sửa đề: \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x^2-1}\)

\(=\dfrac{8+2x^2-2+x^2+3}{\left(x^2+3\right)\left(x^2-1\right)}\)

\(=\dfrac{3x^2+9}{\left(x^2+3\right)\left(x^2-1\right)}=\dfrac{3}{x^2-1}\)

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

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

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