Math Help - how to find the Domain definition of Function

1. how to find the Domain definition of Function

you can see the Function in the picture.

what is the way to find the Domain definition ?

thanks.

2. Factorise the denominator. The function will be continuous everywhere except where the denominator is 0.

3. YES i know if there 0 in the Denominator so the Factorise are not continuous but Can have more points in the denominator to compare it to zero .

how i find Them?

thanks.

4. So your question really is "How do I factor $x^4- 3x^3+ 9x^2- 7x$?" It would have been better to say that in your first post.

"x" is an obvious factor: $x^4- 3x^3+ 9x^2- 7x= x(x^3- 3x^2+ 9x- 7)$. Now the only possible zeros of $x^3- 3x^2+ 9x- 7$ are 1, -1, 7, and -7 (because if it were to factor as (x-a)(x-b)(x-c) the last term would be abc=-7- and the only integer factors of 7 are 1 and 7). Trying x= 1 in the polynomial we get $1^3- 3(1^2)+ 9(1)- 7= 1- 3+ 9- 7= 0$. That tells us that x- 1 is also a factor. Dividing $x^3- 3x^2+ 9x- 7$ by x- 1 leaves $x^2- 2x+ 7$ which has discriminant ( $b^2- 4ac$) equal to $(-2)^2- 4(1)(7)= 4- 28= -24$ so there are no more real number zeros of the polynomial. $x^4- 3x^3+ 9x^2- 7x= x(x-1)(x^2- 2x+ 7)$.

5. thank you.

and yes i mean How do I factor.