algebra equations

Question

(x+6)(x-2)           6x          

__________  X   _______   divide   x-2

2x (x=3)             X=6                  _____          

                                                     2

                                                     

Answer 1

I think the + , are replaced wrongly by  = ( shift character).

 

   ( X +6 ) ( X -2) .     6x           ÷  X - 2      =

    2X ( X +3 )           X +6             2

 

      (X +6 ) ( X -2 ) .  6X        .   2        =

       2X ( X+3 )           X + 6       X- 2

 

          12 X         =  6    
      2 X ( X +3 )     X + 3 

Answer 2

Dividing by (x-2)/2 is the same as multiplying by 2/(x-2), so:

 

f(x) = ((x+6)(x-2)(6x)(2)) / ((2x)(x-3)(x-6)(x-2))

 

Can't divide by zero, so x ≠ 0,2,3,6.

 

x/x is 1 except when x = 0 where it is undefined,

so there is a hole at x = 0.

Same for (x-2)/(x-2) with a hole at x = 2.

 

x = 3 and x = 6 are vertical asymptotes.

 

f(x) = ((x+6)(x-2)(6x)(2)) / ((2x)(x-3)(x-6)(x-2)), x ≠ 0,2,3,6

 

f(x) = 6x(x+6)(x-2)/(x(x-2)(x-3)(x-6)), x ≠ 0,2,3,6

 

f(x) = ((x+6)(6)) / ((x-3)(x-6)), x ≠ 0,2,3,6

 

f(x) = 6(x+6)/((x-3)(x-6)), x ≠ 0,2,3,6

 

f(-6) = 0 is the x-intercept.

 

The holes' y-values are:

x = 0: y = 6(6)/((-3)(-6)) = 2*3*6/(3*6) = 2

x = 2: y = 6(2+6)/((2-3)(2-6)) = 6(8)/((-1)(-4)) = 12

 

See a graph of f(x) here:

http://www.dropbox.com/s/wfuvu2yuj2b37ye/sks23cu14012802.png

Answer 3

Sorry but this does not make much sense. There are two equals signs in your denominators. I know that it is very difficult to input math information with this editor, but  please check your symbols, and submit with question again.  Thank you.