Quy đồng mẫu thức các phân số sau: 5x^2/ x^3 + 6x^2 + 12x +8

* Hướng dẫn giải

$\frac{5{\mathrm{x}}^2}{{\mathrm{x}}^3+6{\mathrm{x}}^2+12\mathrm{x}+8};\frac{4}{{\mathrm{x}}^2+4\mathrm{x}+4};\frac{3}{2\mathrm{x}+4}$

Hay $\frac{5{\mathrm{x}}^2}{{\left(\mathrm{x}+2\right)}^3};\frac{4}{{\left(\mathrm{x}+2\right)}^2};\frac{3}{2\left(\mathrm{x}+2\right)}. \mathrm{MTC}:2{\left(\mathrm{x}+2\right)}^3$

Nhân tử phụ:

$\begin{array}{l}2{\left(\mathrm{x}+2\right)}^3:{\left(\mathrm{x}+2\right)}^3=2\\ 2{\left(\mathrm{x}+2\right)}^3:{\left(\mathrm{x}+2\right)}^2=2\left(\mathrm{x}+2\right)\\ 2{\left(\mathrm{x}+2\right)}^3:2\left(\mathrm{x}+2\right)={\left(\mathrm{x}+2\right)}^2\end{array}$

Quy đồng:

$\begin{array}{l}\frac{5{\mathrm{x}}^2}{{\left(\mathrm{x}+2\right)}^3}=\frac{5{\mathrm{x}}^2.2}{2{\left(\mathrm{x}+2\right)}^3}=\frac{10{\mathrm{x}}^2}{2{\left(\mathrm{x}+2\right)}^3}\\ \frac{4}{{\left(\mathrm{x}+2\right)}^2}=\frac{4.2\left(\mathrm{x}+2\right)}{2{\left(\mathrm{x}+2\right)}^3}=\frac{8\left(\mathrm{x}+2\right)}{2{\left(\mathrm{x}+2\right)}^3}\\ \frac{3}{2\left(\mathrm{x}+2\right)}=\frac{3{\left(\mathrm{x}+2\right)}^2}{2{\left(\mathrm{x}+2\right)}^3}\end{array}$