Toán Lớp 8: $\frac{x}{x^2-36}$ +$\frac{x-6}{x^2+6x}$ -$\frac{36}{(x^2-6x)(x+6)}$
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Toán Lớp 8: $\frac{x}{x^2-36}$ +$\frac{x-6}{x^2+6x}$ -$\frac{36}{(x^2-6x)(x+6)}$
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\dfrac{x}{{{x^2} – 36}} + \dfrac{{x – 6}}{{{x^2} + 6x}} – \dfrac{{36}}{{\left( {{x^2} – 6x} \right)\left( {x + 6} \right)}}\\
= \dfrac{x}{{\left( {x – 6} \right)\left( {x + 6} \right)}} + \dfrac{{x – 6}}{{x\left( {x + 6} \right)}} – \dfrac{{36}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{{x.x}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}} + \dfrac{{\left( {x – 6} \right)\left( {x – 6} \right)}}{{x\left( {x + 6} \right)\left( {x – 6} \right)}} – \dfrac{{36}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{{{x^2}}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}} + \dfrac{{{x^2} – 12x + 36}}{{x\left( {x + 6} \right)\left( {x – 6} \right)}} – \dfrac{{36}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{{{x^2} + {x^2} – 12x + 36 – 36}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{{2{x^2} – 12x}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{{2x\left( {x – 6} \right)}}{{x\left( {x – 6} \right)\left( {x + 6} \right)}}\\
= \dfrac{2}{{x + 6}}
\end{array}\]