Remember to check for extraneous solutions 1/(x-6)=(3x+12)/(x^2-6x) - (6x-24)/(x^2-6x) a) {-1} b) {9} c) {-3} d) {3,-3}

B

Explanation:

RESTRICTIONS: x(x-6)≠0  ⇒ x ≠ 0 and x ≠ 6

x = 3x + 12 - (6x - 24)

x = 3x + 12 - 6x + 24

x = -3x + 36

4x = 36

x = 9

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional