SOLUTION: <pre><b>Multiply or Divide <u> 1-2/3z </u> z-4/9z</pre>

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Question 38546This question is from textbook Algebra 2 with trig
: 
Multiply or Divide 
                  1-2/3z 
                  z-4/9z
 This question is from textbook Algebra 2 with trig

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply or Divide

Multiply or Divide 
                  1-2/3z 
                  z-4/9z


You did not put parentheses around your denominators,
so your expression as written means this


                          2
                     1 - ——— z 
                          3
                    ———————————
                          4
                     z - ——— z 
                          9

However I think you intended it to be this:

                           2
                     1 - ———— 
                          3z
                    ———————————
                           4
                     z - ———— 
                          9z

So I will assume this is what you meant.
Put 1's under the 1 and z

                      1      2
                     ——— - ———— 
                      1     3z
                    —————————————
                      z      4
                     ——— - ———— 
                      1     9z

The four denominators are 1, 3z, 1 and 9z.
Their LCD is 9z so multiply top and bottom 
by (9z)/(9z), putting 1's under the 9z's


               9z  æ 1      2 ö
              ———— į——— - ————ũ 
                1  č 1     3z ø 
            —————— —————————————
               9z  æ z      4 ö
              ———— į——— - ————ũ 
                1  č 1     9z ø

Remove the parentheses by distributing:

              9z   1     9z    2 
             ————Ũ——— - ————Ũ———— 
               1   1      1   3z 
            ———————————————————————
              9z   z     9z    4 
             ————Ũ——— - ————Ũ———— 
               1   1      1   9z 

Cancel 3z into 9z on the top right, and
cancel the 9z's on the bottom right

                          3
              9z   1     9z    2 
             ————Ũ——— - ————Ũ———— 
               1   1      1   13z 
            ———————————————————————
              9z   z     19z    4 
             ————Ũ——— - ————Ũ———— 
               1   1      1   19z 
 

                   9z - 6
                 —————————
                  9zē - 4

Factor numerator and denominator:

                   3(3z - 2)
               ————————————————
               (3z - 2)(3z + 2)

Cancel the (3z - 2)'s

                        1
                   3(3z - 2)
               ————————————————
               (3z - 2)(3z + 2)
                   1

                       3
                   ————————
                    3z + 2

Edwin
AnlytcPhil@aol.com