Question

[nguyễn ngọc minh ánh]

quy đồng mẫu thức

3 / x mũ 3 - 1 , 2x / x mũ 2 + x + 1 ,  x / x- 1

Answer 1

[l҉o҉n҉g҉ d҉z҉]

\(\frac{3}{x^3-1}=\frac{3}{\left(x-1\right)\left(x^2+x+1\right)}\)( ĐKXĐ : x ≠ 1 )

\(\frac{2x}{x^2+x+1}\)( ĐKXĐ : x ∈ R )

\(\frac{x}{x-1}\)( ĐKXĐ : x ≠ 1 )

MTC : ( x - 1 )( x² + x + 1 )

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

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

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