Toán Lớp 8: Quy đồng mẫu thức $\frac{1}{x^{2}-3x+2}$;$\frac{1}{2x^{2}+3x-5}$
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Toán Lớp 8: Quy đồng mẫu thức $\frac{1}{x^{2}-3x+2}$;$\frac{1}{2x^{2}+3x-5}$
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+ ){x^2} – 3x + 2\\
= {x^2} – x – 2x + 2\\
= \left( {x – 1} \right)\left( {x – 2} \right)\\
+ )2{x^2} + 3x – 5\\
= 2{x^2} + 5x – 2x – 5\\
= \left( {2x + 5} \right)\left( {x – 1} \right)\\
\Leftrightarrow MSC = \left( {x – 1} \right)\left( {x – 2} \right)\left( {2x + 5} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{1}{{{x^2} – 3x + 2}} = \dfrac{{2x + 5}}{{\left( {x – 1} \right)\left( {x – 2} \right)\left( {2x + 5} \right)}}\\
\dfrac{1}{{2{x^2} + 3x – 5}} = \dfrac{{x – 2}}{{\left( {x – 1} \right)\left( {x – 2} \right)\left( {2x + 5} \right)}}
\end{array} \right.
\end{array}$