Toán Lớp 9: Rút gọn A= √x/ √x+3 – √x + 3/ √x-3 + x+11 √x+6/9-x
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Toán Lớp 9: Rút gọn A= √x/ √x+3 – √x + 3/ √x-3 + x+11 √x+6/9-x
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A = \dfrac{{\sqrt x }}{{\sqrt x + 3}} – \dfrac{{\sqrt x + 3}}{{\sqrt x – 3}} + \dfrac{{x + 11\sqrt x + 6}}{{9 – x}}\\
= \dfrac{{\sqrt x }}{{\sqrt x + 3}} – \dfrac{{\sqrt x + 3}}{{\sqrt x – 3}} – \dfrac{{x + 11\sqrt x + 6}}{{x – 9}}\\
= \dfrac{{\sqrt x \left( {\sqrt x – 3} \right) – {{\left( {\sqrt x + 3} \right)}^2} – x – 11\sqrt x – 6}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{x – 3\sqrt x – x – 6\sqrt x – 9 – x – 11\sqrt x – 6}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{x – 20\sqrt x – 15}}{{\left( {\sqrt x – 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{x – 20\sqrt x – 15}}{{x – 9}}
\end{array}$