Question

Tính: \(\frac{x^2+3xy+2y^2}{5x^2+4xy-y^2}-\frac{x^2-5xy+4y^2}{-2x^2+4xy-2y^2}\)

Answer 1

\(\frac{x^2+3xy+2y^2}{5x^2+4xy-y^2}-\frac{x^2-5xy+4y^2}{-2x^2+4xy-2y^2}\)

\(=\frac{x+2y}{5x-y}-\left[-\frac{x-4y}{2\left(x-y\right)}\right]\)

\(=\frac{x+2y}{5x-y}+\frac{x-4y}{2\left(x-y\right)}\)

\(=\frac{\left(x+2y\right).2\left(x-y\right)}{\left(5x-y\right).2\left(x-y\right)}+\frac{\left(x-4y\right).\left(5x-y\right)}{2\left(x-y\right).\left(5x-y\right)}\)

\(=\frac{\left(x+2y\right).2\left(x-y\right)+\left(x-4y\right).\left(5x-y\right)}{2\left(x-y\right).\left(5x-y\right)}\)

\(=\frac{7x^2-19xy}{2\left(x-y\right).\left(5x-y\right)}\)