Question

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Answer 1

\[\begin{array}{l}
A = \frac{3}{{2x - 3}} + \frac{x}{{x - 2}} + \frac{{9x - 10}}{{4 - {x^2}}}\\
dk:\left\{ \begin{array}{l}
2x - 3 \ne 0\\
x - 2 \ne 0\\
4 - {x^2} \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne \frac{3}{2}\\
x \ne \pm 2
\end{array} \right.\\
A = \frac{3}{{2x - 3}} + \frac{{x(x + 2)}}{{(x - 2)(x + 2)}} - \frac{{9x - 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} + 2x - 9x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} - 7x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} - 2x - 5x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{x(x - 2) - 5(x - 2)}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{(x - 2)(x - 5)}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{x - 5}}{{x + 2}}\\
= \frac{{3(x + 2) + (x - 5)(2x - 3)}}{{(2x - 3)(x + 2)}}\\
= \frac{{3x + 6 + 2{x^2} - 3x - 10x + 15}}{{(2x - 3)(x + 2)}}\\
= \frac{{2{x^2} - 10x + 21}}{{(2x - 3)(x + 2)}}
\end{array}\]

Vậy với \[\left\{ \begin{array}{l}
x \ne \frac{3}{2}\\
x \ne \pm 2
\end{array} \right.\] thì \[A = \frac{{2{x^2} - 10x + 21}}{{(2x - 3)(x + 2)}}\]

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Answer 2

\[\begin{array}{l}
A = \frac{3}{{2x - 3}} + \frac{x}{{x - 2}} + \frac{{9x - 10}}{{4 - {x^2}}}\\
dk:\left\{ \begin{array}{l}
2x - 3 \ne 0\\
x - 2 \ne 0\\
4 - {x^2} \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne \frac{3}{2}\\
x \ne \pm 2
\end{array} \right.\\
A = \frac{3}{{2x - 3}} + \frac{{x(x + 2)}}{{(x - 2)(x + 2)}} - \frac{{9x - 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} + 2x - 9x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} - 7x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{{x^2} - 2x - 5x + 10}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{x(x - 2) - 5(x - 2)}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{(x - 2)(x - 5)}}{{(x - 2)(x + 2)}}\\
= \frac{3}{{2x - 3}} + \frac{{x - 5}}{{x + 2}}\\
= \frac{{3(x + 2) + (x - 5)(2x - 3)}}{{(2x - 3)(x + 2)}}\\
= \frac{{3x + 6 + 2{x^2} - 3x - 10x + 15}}{{(2x - 3)(x + 2)}}\\
= \frac{{2{x^2} - 10x + 21}}{{(2x - 3)(x + 2)}}
\end{array}\]

Vậy với \[\left\{ \begin{array}{l}
x \ne \frac{3}{2}\\
x \ne \pm 2
\end{array} \right.\] thì \[A = \frac{{2{x^2} - 10x + 21}}{{(2x - 3)(x + 2)}}\]

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