limx→ a[(1)/(x²-3ax+2a²)+(1)/(2x²-3ax+a²)]

7.2 Q.III · Q36

\displaystyle\lim_{x\to a}\left[\frac{1}{x^2-3ax+2a^2}+\frac{1}{2x^2-3ax+a^2}\right]

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$x^2-3ax+2a^2=(x-a)(x-2a)$ and $2x^2-3ax+a^2=(2x-a)(x-a)$ . So the sum is $\dfrac{1}{(x-a)(x-2a)}+\dfrac{1}{(x-a)(2x-a)}=\dfrac{1}{x-a}\left[\dfrac{1}{x-2a}+\dfrac{1}{2x-a}\right]=\dfrac{1}{x-a}\cdot\dfrac{(2x-a)+(x-2a)}{(x-2a)(2x-a)}=\dfrac{1}{x-a}\cdot\dfrac{3x-3a}{(x-2a)(2x-a)}=\dfrac{1}{x-a}\cdot\dfrac{3(x-a)}{(x-2a)(2x-a)}=\dfrac{3 …

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Q. $\displaystyle\lim_{x\to a}\left[\frac{1}{x^2-3ax+2a^2}+\frac{1}{2x^2-3ax+a^2}\right]$

Concept understanding — Limits by Factorization

Q.lim⁡x→a[1x2−3ax+2a2+12x2−3ax+a2]\displaystyle\lim_{x\to a}\left[\frac{1}{x^2-3ax+2a^2}+\frac{1}{2x^2-3ax+a^2}\right]x→alim​[x2−3ax+2a21​+2x2−3ax+a21​]

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Q. $\displaystyle\lim_{x\to a}\left[\frac{1}{x^2-3ax+2a^2}+\frac{1}{2x^2-3ax+a^2}\right]$

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