Question

Cộng các phân tử:

a)\(\dfrac{2x-3}{x}+\dfrac{1-x}{x+2}+\dfrac{4x}{x-1}\)

b)\(\dfrac{1}{1+x}+\dfrac{1}{x-1}+\dfrac{3x}{1-x^2}\)

c)\(\dfrac{x^3}{x+1}+\dfrac{x^2}{x-1}+\dfrac{1}{x+1}+\dfrac{1}{x-1}\)

d)\(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)

Answer 1

b: \(=\dfrac{x-1+x+1-3x}{\left(x+1\right)\left(x-1\right)}=\dfrac{-x}{\left(x+1\right)\left(x-1\right)}\)

c: \(=\dfrac{x^3+1}{x+1}+\dfrac{x^2+1}{x-1}\)

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

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

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

d: \(=\dfrac{2x+y}{x\left(2x-y\right)}-\dfrac{16x}{\left(2x-y\right)\left(2x+y\right)}+\dfrac{2x-y}{x\left(2x+y\right)}\)

\(=\dfrac{4x^2+4xy+y^2-16x^2+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)

\(=\dfrac{-8x^2+2y^2}{x\left(2x-y\right)\left(2x+y\right)}=\dfrac{-2\left(4x^2-y^2\right)}{x\left(2x-y\right)\left(2x+y\right)}=\dfrac{-2}{x}\)