Question

1 , thực hiện các phép tính sau

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

b,\(\dfrac{5x-2y}{x2-y2}\)+\(\dfrac{y-4x}{x2-y2}\)

c,\(\dfrac{x-1}{12x}\)+\(\dfrac{2x+7}{12x}\)+\(\dfrac{6-3x}{12x}\)

Answer 1

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

b, \(\dfrac{5x-2y}{x^2-y^2}+\dfrac{y-4x}{x^2-y^2}=\dfrac{5x-2y+y-4x}{\left(x+y\right)\left(x-y\right)}=\dfrac{x-y}{\left(x+y\right)\left(x-y\right)}=\dfrac{1}{x+y}\)

c, \(\dfrac{x-1}{12x}+\dfrac{2x+7}{12x}+\dfrac{6-3x}{12x}=\dfrac{x-1+2x+7+6-3x}{12x}=\dfrac{12}{12x}=\dfrac{1}{x}\)

Answer 2

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

b,\(\dfrac{5x-2y+y-4x}{\left(x+y\right)\left(x-y\right)}\)=\(\dfrac{x-y}{\left(x+y\left(x-y\right)\right)}\)

c,\(\dfrac{x-1+2x+7+6-3x}{12x}\)=\(\dfrac{12}{12x}\)=\(\dfrac{1}{x}\)

Answer 3

\(a,\dfrac{x+1}{3}+\dfrac{2x-1}{3}=\dfrac{x+1+2x-1}{3}=\dfrac{3x}{3}=x\)\(b,\dfrac{5x-2y}{x^2-y^2}+\dfrac{y-4x}{x^2-y^2}=\dfrac{5x-2y+y-4x}{x^2-y^2}=\dfrac{x-y}{\left(x+y\right).\left(x-y\right)}=\dfrac{1}{x+y}\)\(c,\dfrac{x-1}{12x}+\dfrac{2x+7}{12x}+\dfrac{6-3x}{12x}=\dfrac{x-1+2x+7+6-3x}{12x}=\dfrac{12}{12x}=\dfrac{1}{x}\)