limx→ 1[(x+2)/(x²-5x+4)+(x-4)/(3(x²-3x+2))]

7.2 Q.III · Q35

\displaystyle\lim_{x\to 1}\left[\frac{x+2}{x^2-5x+4}+\frac{x-4}{3(x^2-3x+2)}\right]

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$x^2-5x+4=(x-1)(x-4)$ and $x^2-3x+2=(x-1)(x-2)$ . Common denominator $3(x-1)(x-4)(x-2)$ . Combined numerator: $3(x+2)(x-2)+(x-4)^2=3(x^2-4)+(x^2-8x+16)=4x^2-8x+4=4(x-1)^2$ . So the expression is $\dfrac{4(x-1)^2}{3(x-1)(x-4)(x-2)}=\dfrac{4(x-1)}{3(x …

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Q. $\displaystyle\lim_{x\to 1}\left[\frac{x+2}{x^2-5x+4}+\frac{x-4}{3(x^2-3x+2)}\right]$

Concept understanding — Limits by Factorization

Q.lim⁡x→1[x+2x2−5x+4+x−43(x2−3x+2)]\displaystyle\lim_{x\to 1}\left[\frac{x+2}{x^2-5x+4}+\frac{x-4}{3(x^2-3x+2)}\right]x→1lim​[x2−5x+4x+2​+3(x2−3x+2)x−4​]

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Q. $\displaystyle\lim_{x\to 1}\left[\frac{x+2}{x^2-5x+4}+\frac{x-4}{3(x^2-3x+2)}\right]$

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