Toán rút gọn a √a + 27/a-9 + a-9/( √a – 3 ) ² 29/07/2021 By Iris rút gọn a √a + 27/a-9 + a-9/( √a – 3 ) ²
Đáp án: $\begin{array}{l}\dfrac{{a\sqrt a + 27}}{{a – 9}} + \dfrac{{a – 9}}{{{{\left( {\sqrt a – 3} \right)}^2}}}\\ = \dfrac{{\left( {\sqrt a + 3} \right)\left( {a – 3\sqrt a + 9} \right)}}{{\left( {\sqrt a + 3} \right)\left( {\sqrt a – 3} \right)}} + \dfrac{{\left( {\sqrt a – 3} \right)\left( {\sqrt a + 3} \right)}}{{{{\left( {\sqrt a – 3} \right)}^2}}}\\ = \dfrac{{a – 3\sqrt a + 9}}{{\sqrt a – 3}} + \dfrac{{\sqrt a + 3}}{{\sqrt a – 3}}\\ = \dfrac{{a – 2\sqrt a + 12}}{{\sqrt a – 3}}\end{array}$ Trả lời
Đáp án:
$\begin{array}{l}
\dfrac{{a\sqrt a + 27}}{{a – 9}} + \dfrac{{a – 9}}{{{{\left( {\sqrt a – 3} \right)}^2}}}\\
= \dfrac{{\left( {\sqrt a + 3} \right)\left( {a – 3\sqrt a + 9} \right)}}{{\left( {\sqrt a + 3} \right)\left( {\sqrt a – 3} \right)}} + \dfrac{{\left( {\sqrt a – 3} \right)\left( {\sqrt a + 3} \right)}}{{{{\left( {\sqrt a – 3} \right)}^2}}}\\
= \dfrac{{a – 3\sqrt a + 9}}{{\sqrt a – 3}} + \dfrac{{\sqrt a + 3}}{{\sqrt a – 3}}\\
= \dfrac{{a – 2\sqrt a + 12}}{{\sqrt a – 3}}
\end{array}$