Question

Thực hiện phép tinh và rút gọn:

\(a.\frac{x+y}{x-y}+\frac{x^2-4y^2}{x^2-y^2}-\frac{x-3y}{x+y}\)

Answer 1

\(\frac{x+y}{x-y}+\frac{x^2-4y^2}{x^2-y^2}-\frac{x-3y}{x+y}\)

\(=\frac{\left(x+y\right)^2}{\left(x+y\right)\left(x-y\right)}+\frac{x^2-4y^2}{\left(x-y\right)\left(x+y\right)}-\frac{\left(x-3y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}\)

\(=\frac{x^2+2xy+y^2+x^2-4y^2-x^2+xy+3xy-3y^2}{\left(x+y\right)\left(x-y\right)}\)

\(=\frac{x^2+6xy-6y^2}{\left(x+y\right)\left(x-y\right)}\)

Tham khảo nhé~