Question

cho biểu thức

P =\(\left(\dfrac{1}{2x-y}+\dfrac{3y}{y^2-4x^2}-\dfrac{2}{2x+y}\right)\)

a) rút gọn P

b) tìm x để P=\(\dfrac{1}{2}\)

Answer 1

a) P = (\(\dfrac{1}{2x-y}\) + \(\dfrac{3y}{y^2-4x^2}\) - \(\dfrac{2}{2x+y}\) )

= (\(\dfrac{1}{2x-y}\) - \(\dfrac{3y}{4x^2-y^2}\) - \(\dfrac{2}{2x+y}\) )

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

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