Question

Quy đồng mẫu thức các phân thức

1). \(\dfrac{4x^2-3x+5}{x^3-1}\); \(\dfrac{1-2x}{x^2+x+1}\); -2

2). \(\dfrac{10}{x+2}\); \(\dfrac{5}{2x-4}\); \(\dfrac{1}{6-3x}\)

Answer 1

1)

\(\dfrac{4x^2-3x+5}{x^3-1}=\dfrac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)

MTC: \(\left(x-1\right)\left(x^2+x+1\right)\)

\(\dfrac{4x^2-3x+5}{x^3-1}=\dfrac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)

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

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