1. which domain restrictions apply to the rational expression? x^2+5x+6 x^2-9 select each correct answer. x≠2 x≠1 x≠−3 x≠3 x≠−2 x≠−1 (4x)/(x-3)+(2)/(x^(2)-9)= (1)/(x+3) a. 19/3 b. 13/3 c. -5 d. -17/3 9. which statement best reflects the solution(s) of the equation? 1/x + 1/x-3 = x-2 / x-3 a. there is only one solution: x = 1. the solution x = 0 is an extraneous solution. b. there is only one solution: x = 1. the solution x = 3 is an extraneous solution. c. there is only one solution: x = 3. the solution x = 1 is an extraneous solution. d. there are two solutions: x = 1 and x = 3. 10. (√3x+1)−x+3=0 a. there is only one solution: x = 1. the solution x = 8 is an extraneous solution. b. there is only one solution: x = 8. the solution x = 1 is an extraneous solution. c. there is only one solution: x = 8. the solution x = 0 is an extraneous solution. d. there are two solutions: x = 1 and x = 8.

Answer with explanation:

1. The given rational expression is

The function is not defined ,when

 →(x-3)(x+3)=0

→x-3≠0 ∧ x+3≠0

→x≠3, ∧ x ≠ -3

⇒Option C and D

→x≠−3

→x≠3

2.

None of the option

3.

For, x=3 , the equation is not defined.

So, there is single solution which is , x=1.

Option B:→ There is only one solution: x = 1.

The solution x = 3 is an extraneous solution.

4.

None of the option

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

b. x- 48 =120

step-by-step explanation: