Question

limt x=3 hai kisi ko bhi answer ata ho to send kar​

Answer 1

Step-by-step explanation:

$\lim_{x\to 3} [ \frac{1}{3 {x}^{2} - 14x + 15 } + \frac{1}{{x}^{2} - 10x + 21 }] \\ \\ = \lim_{x\to 3} [ \frac{1}{3 {x}^{2} - 9x - 5x + 15 } + \frac{1}{{x}^{2} - 7x - 3x+ 21 }] \\ \\ = \lim_{x\to 3} [ \frac{1}{3x(x - 3) - 5(x - 3) } + \frac{1}{x({x}- 7) - 3(x - 7) }] \\ \\ = \lim_{x\to 3} [ \frac{1}{(x - 3)(3x - 5) } + \frac{1}{(x - 3)(x - 7) }] \\ \\ = \lim_{x\to 3} [ \frac{1}{(x - 3)} \{\frac{1}{(3x - 5) } + \frac{1}{(x - 7) } \}] \\ \\ = \lim_{x\to 3} [ \frac{1}{(x - 3)} \{\frac{x - 7 + 3x - 5}{(3x - 5) (x - 7)} \}] \\ \\ = \lim_{x\to 3} [ \frac{1}{(x - 3)} \{\frac{4x - 12}{(3x - 5) (x - 7)} \}] \\ \\ = \lim_{x\to 3} [ \frac{1}{(x - 3)} \{\frac{4(x - 3)}{(3x - 5) (x - 7)} \}] \\ \\ = \lim_{x\to 3} [ \{\frac{4}{(3x - 5) (x - 7)} \}] \\\\ = \frac{4}{(3 \times 3 - 5) (3- 7)} (applying \: limit )\\\\ = \frac{4}{(9 - 5) ( - 4)} \\\\ = \frac{4}{(4) ( - 4)} \\ \\ = - \frac{1}{4}$