Đáp án:
e) \(\dfrac{{{x^4} + 5{x^3} + 12{x^2} + 18x}}{{{x^4} + 4{x^3} - 7{x^2} - 4x + 6}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{x + 5}}{{x - 6}}.\dfrac{{{x^2} + 2x + 2}}{{x - 3}} = \dfrac{{{x^3} + 2{x^2} + 2x + 5{x^2} + 10x + 10}}{{{x^2} - 9x + 18}}\\
= \dfrac{{{x^3} + 7{x^2} + 12x + 10}}{{{x^2} - 9x + 18}}\\
c)\dfrac{{{x^2} + 1}}{{x - 1}}.\dfrac{{x + 1}}{{x + 1}} = \dfrac{{{x^2} + 1}}{{x - 1}}\\
e)\dfrac{{{x^2} + 2x + 6}}{{{x^2} - 1}}.\dfrac{{{x^2} + 3x}}{{{x^2} + 4x - 6}}\\
= \dfrac{{{x^4} + 3{x^3} + 2{x^3} + 6{x^2} + 6{x^2} + 18x}}{{{x^4} + 4{x^3} - 6{x^2} - {x^2} - 4x + 6}}\\
= \dfrac{{{x^4} + 5{x^3} + 12{x^2} + 18x}}{{{x^4} + 4{x^3} - 7{x^2} - 4x + 6}}
\end{array}\)
