Rational expressions
(for what value of x is the rational expression below undefined)?
3x-12/9-x

For x = 9  the given rational expression  is undefined.

Step-by-step explanation:

Given rational expression

We have to find for what value of x is the given rational expression is undefined.

Consider the given rational expression

For a fractional expression to be undefined the denominator has to be zero, so that

Thus, for the given expression

Denominator is 9-x

Thus, to make it not defined, Put 9 - x = 0

⇒ x = 9

Thus, for x = 9  the given rational expression  is undefined.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above