Question

bài 2 : tính nhanh

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

Answer 1

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

\(=\dfrac{3x^2+9x+6}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)

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

Answer 2

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

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

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

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