You can
put this solution on YOUR website! Simplify each complex fraction
(1/3-1/4)/(1/3+1/6)
1 1
——— - ———
3 4
———————————
1 1
——— + ———
3 6
Look at all four denominators 3,4,3,and 6. The LCD of all
four of these is 12. Therefore we multiply every fraction
in the top and in the bottom by 12/1
12 1 12 1
———— · ——— - ———— · ———
1 3 1 4
—————————————————————————
12 1 12 1
———— · ——— + ———— · ———
1 3 1 6
Now we cancel:
4 3
12 1 12 1
———— · ——— - ———— · ———
1 31 1 4 1
—————————————————————————
412 1 212 1
———— · ——— + ———— · ———
1 31 1 61
All that's left is:
4 - 3
———————
4 + 2
or
1
———
6
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===================================================
1 3
——— - ———
x 2
———————————
3 1
——— + ———
4 x
Look at all four denominators x,2,4,and x. The LCD of all
four of these is 4x. Therefore we multiply every fraction
in the top and in the bottom by 4x/1
4x 1 4x 3
———— · ——— - ———— · ———
1 x 1 2
—————————————————————————
4x 3 4x 1
———— · ——— + ———— · ———
1 4 1 x
Now we cancel:
2
4x 1 4x 3
———— · ——— - ———— · ———
1 x1 1 21
—————————————————————————
14x 3 24x 1
———— · ——— + ———— · ———
1 41 1 x1
All that's left is:
4 - 2x·3
——————————
x·3 + 4
or
4 - 6x
————————
3x + 4
Edwin
AnlytcPhil@aol.com
