Question

Thực hiện phép tính:

a, \(\dfrac{y}{xy-5x^2}-\dfrac{15y-25x}{y^2-25x^2}\)

\(b,\dfrac{2x}{x^2+2xy}-\dfrac{y}{2y^2-xy}+\dfrac{4y}{x^2-4y^2}\)

Answer 1

a) \(\dfrac{y}{xy-5x^2}-\dfrac{15y-25x}{y^2-25x^2}=\dfrac{y}{x\left(y-5x\right)}-\dfrac{15y-25x}{\left(y-5x\right)\left(y+5x\right)}\)

\(=\dfrac{y\left(y+5x\right)}{x\left(y-5x\right)\left(y+5x\right)}-\dfrac{x\left(15y-25x\right)}{x\left(y-5x\right)\left(y+5x\right)}\)

\(=\dfrac{y^2+5xy-15xy+25x^2}{x\left(y-5x\right)\left(y+5x\right)}\)

\(=\dfrac{y^2-10xy+25x^2}{x\left(y-5x\right)\left(y+5x\right)}\)

\(=\dfrac{\left(y-5x\right)^2}{x\left(y-5x\right)\left(y+5x\right)}\)

\(=\dfrac{y-5x}{x\left(y+5x\right)}\)

Answer 2

b: \(=\dfrac{2}{x+2y}-\dfrac{1}{2y-x}+\dfrac{4y}{\left(x-2y\right)\left(x+2y\right)}\)

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