Question

[Quốc Bình]

1) thực hiện phép tính

a) \(\dfrac{x-3}{4x+4}-\dfrac{x-1}{6x-30}\)

b) \(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\)

c) \(\dfrac{x+9y}{x^2-9y^2}-\dfrac{3y}{x^2-3xy}\)

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

e) \(\dfrac{3\left(x-2\right)}{x^2-2x+1}-\dfrac{6}{x^2-1}-\dfrac{3x-2}{1-x^2}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

b: \(=\dfrac{-1}{x\left(5x-1\right)}-\dfrac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)

\(=\dfrac{-5x-1-25x^2+15x}{x\left(5x-1\right)\left(5x+1\right)}\)

\(=\dfrac{-25x^2-10x-1}{x\left(5x-1\right)\left(5x+1\right)}=\dfrac{-\left(5x+1\right)}{x\left(5x-1\right)}\)

c: \(=\dfrac{x+9y}{\left(x-3y\right)\left(x+3y\right)}-\dfrac{3y}{x\left(x-3y\right)}\)

\(=\dfrac{x^2+9xy-3xy-9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)

\(=\dfrac{x^2+6xy-9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)

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

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

\(=\dfrac{3x^2+8x-3}{\left(x-1\right)^2\cdot\left(x+1\right)}=\dfrac{3x^2+9x-x-3}{\left(x-1\right)^2\cdot\left(x+1\right)}\)

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