Question

Find the domain of the function

i - $\frac{ {x}^{2} + 3x + 5}{ {x}^{2} - 5x + 4 }$

ii - $\frac{ {x}^{2} + 2x + 1}{ {x}^{2} - 8x + 12 }$
​

Answer 1

Hope it's Helpful for you.....

Answer 2

Step-by-step explanation:

1.)

y = (x² + 3x + 5)/(x² - 5x + 4)

= (x² + 3x + 5)/(x² - 4x - x +4)

= (x² + 3x + 5)[x(x-4) - 1(x-4)]

= (x² + 3x + 5)(x-4)(x-1)

So domain is all real values of x except x=4 & x=1

2.)

y = (x² + 2x + 1)/(x² - 8x + 12)

= (x² + 2x +1)/(x² -2x -6x+12)

= (x² +2x +1)/(x-2)(x-6)

Clearly domain is all real values except 2 or 6

NOTE : IN PREVIOUS ANSWER RANGE = [0, ∞) for |x+5|