Question

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

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

c)\(\dfrac{y-12}{6y-36}+\dfrac{6}{y^2-6y}\)

d)\(\dfrac{6+x}{x+3x}+\dfrac{3}{2x+6}\)

Answer 1

a) \(\dfrac{2}{x+3}+\dfrac{1}{x}\) [ MTC: x(x+3) ]

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

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

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

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

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

\(=\dfrac{x+1}{2\left(x-1\right)}+\dfrac{-2x}{\left(x-1\right)\left(x+1\right)}\) \(\left[MTC:2\left(x-1\right)\left(x+1\right)\right]\)

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

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

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

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

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

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

Answer 2

a) Ta có :

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

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

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

c) \(\dfrac{y-12}{6y-36}+\dfrac{6}{y^2-6y}=\dfrac{y-12}{6\left(y-6\right)}+\dfrac{6}{y\left(y-6\right)}\)

\(=\dfrac{y^2-12+36}{6y\left(y-6\right)}=\dfrac{y^2-24}{6y\left(y-6\right)}\)

d) \(\dfrac{6+x}{x+3x}+\dfrac{3}{2x+6}=\dfrac{6+x}{4x}+\dfrac{3}{2\left(x+3\right)}\)

\(=\dfrac{\left(6+x\right)\left(2x+6\right)+12x}{8x\left(x+3\right)}\)(Đề câu này phải sửa thành\(\dfrac{6+x}{x^2+3x}chứ\)) ???