4 / (a+1) +1
-----------------
6 / (a-1) +1
Simplify the complex fraction!?
2008-10-12 8:36 am
回答 (7)
2008-10-12 8:44 am
✔ 最佳答案
4 / (a+1) +1-----------------
6 / (a-1) +1
= (5 + a)(a -- 1) / (5 + a)(a + 1)
= (a -- 1) / (a + 1)
2008-10-12 5:43 pm
= ([4/{a + 1}] + 1)/([6/{a - 1}] + 1)
= ([4 + a + 1]/[a + 1])/([6 + a - 1]/[a - 1])
= ([a + 5]/[a + 1])/([a + 5]/[a - 1])
= ([a + 5]/[a + 1])([a - 1]/[a + 5])
= (a - 1)/(a + 1)
Answer: (a - 1)/(a + 1)
= ([4 + a + 1]/[a + 1])/([6 + a - 1]/[a - 1])
= ([a + 5]/[a + 1])/([a + 5]/[a - 1])
= ([a + 5]/[a + 1])([a - 1]/[a + 5])
= (a - 1)/(a + 1)
Answer: (a - 1)/(a + 1)
2008-10-12 4:41 pm
[4/(a + 1) + 1]/[6/(a - 1) + 1]
= [4/(a + 1) + (a + 1)/(a + 1)]/[6/(a - 1) + (a - 1)/(a - 1)]
= [(a + 5)/(a + 1)]/[(a + 5)/(a - 1)]
= [(a + 5)/(a + 1)][(a - 1)/(a + 5)] (cancel out a + 1)
= (a - 1)/(a + 1)
= [4/(a + 1) + (a + 1)/(a + 1)]/[6/(a - 1) + (a - 1)/(a - 1)]
= [(a + 5)/(a + 1)]/[(a + 5)/(a - 1)]
= [(a + 5)/(a + 1)][(a - 1)/(a + 5)] (cancel out a + 1)
= (a - 1)/(a + 1)
2008-10-12 3:58 pm
I'm going to use brackets and parenthesis for clarity:
[4/(a + 1) + 1] / [6/(a - 1) + 1]
Start multiplying each term by a factor of 1 that will make the denominators. Start with the top part of this problem. The denominators need to be (a + 1):
= [4/(a + 1) + 1*(a + 1)/(a + 1)] / [6/(a - 1) + 1]
= [4 + a + 1)/(a + 1)] / [6/(a - 1) + 1]
= [a + 5)/(a + 1)] / [6/(a - 1) + 1]
Now do the same to the bottom part of the problem. The denominators need to be (a - 1):
= [(a + 5)/(a + 1)] / [6/(a - 1) + (a - 1)/(a - 1)]
= [(a + 5)/(a + 1)] / [(6 + a - 1)/(a - 1)]
= [(a + 5)/(a + 1)] / [(a + 5)/(a - 1)]
Now multiply instead of dividing. To do this, flip the denominator:
= [(a + 5)/(a + 1)] / [(a - 1)/(a + 5)]
Cancel out the (a + 5) terms, and the answer is:
= (a - 1)/(a + 1)
[4/(a + 1) + 1] / [6/(a - 1) + 1]
Start multiplying each term by a factor of 1 that will make the denominators. Start with the top part of this problem. The denominators need to be (a + 1):
= [4/(a + 1) + 1*(a + 1)/(a + 1)] / [6/(a - 1) + 1]
= [4 + a + 1)/(a + 1)] / [6/(a - 1) + 1]
= [a + 5)/(a + 1)] / [6/(a - 1) + 1]
Now do the same to the bottom part of the problem. The denominators need to be (a - 1):
= [(a + 5)/(a + 1)] / [6/(a - 1) + (a - 1)/(a - 1)]
= [(a + 5)/(a + 1)] / [(6 + a - 1)/(a - 1)]
= [(a + 5)/(a + 1)] / [(a + 5)/(a - 1)]
Now multiply instead of dividing. To do this, flip the denominator:
= [(a + 5)/(a + 1)] / [(a - 1)/(a + 5)]
Cancel out the (a + 5) terms, and the answer is:
= (a - 1)/(a + 1)
2008-10-12 3:53 pm
[ ( 4 + (a+1) ) / (a + 1) ] / [ ( 6 + (a - 1) ) / (a - 1) ]
[ ( a + 5 ) / (a + 1) ] / [ ( a + 5 ) / (a - 1) ]
[ (a + 5) (a - 1) ] / [ (a + 1) (a + 5) ]
(a - 1) / (a + 1)
Answer: (a - 1) / (a + 1)
[ ( a + 5 ) / (a + 1) ] / [ ( a + 5 ) / (a - 1) ]
[ (a + 5) (a - 1) ] / [ (a + 1) (a + 5) ]
(a - 1) / (a + 1)
Answer: (a - 1) / (a + 1)
2008-10-12 3:46 pm
4 / (a+1) + 1
-----------------
6 / (a-1) + 1
=
4 / (a+1) + (a + 1)/(a + 1)
---------------------------------
6 / (a-1) + (a - 1)/(a - 1)
=
(4 + a + 1)/(a + 1)
-----------------------
(6 + a - 1)/(a - 1)
=
(5 + a)/(a + 1)
------------------
(5 + a)/(a - 1)
=
1 / (a + 1)
--------------
1 / (a - 1)
=
1 / (a + 1) * (a - 1)
= (a - 1) / (a + 1)
-----------------
6 / (a-1) + 1
=
4 / (a+1) + (a + 1)/(a + 1)
---------------------------------
6 / (a-1) + (a - 1)/(a - 1)
=
(4 + a + 1)/(a + 1)
-----------------------
(6 + a - 1)/(a - 1)
=
(5 + a)/(a + 1)
------------------
(5 + a)/(a - 1)
=
1 / (a + 1)
--------------
1 / (a - 1)
=
1 / (a + 1) * (a - 1)
= (a - 1) / (a + 1)
2008-10-12 3:45 pm
[(4/(a + 1)) + 1]/[(6/(a - 1)) + 1]
= [(4 + a + 1)/(a + 1)]/[(6 + a - 1)/(a - 1)]
= [(5 + a)/(a + 1)]/[(5 + a)/(a - 1)]
= [(5 + a)/(a + 1)][(a - 1)/(5 + a)]
= (a - 1)/(a + 1)
= [(4 + a + 1)/(a + 1)]/[(6 + a - 1)/(a - 1)]
= [(5 + a)/(a + 1)]/[(5 + a)/(a - 1)]
= [(5 + a)/(a + 1)][(a - 1)/(5 + a)]
= (a - 1)/(a + 1)
收錄日期: 2021-05-01 11:23:22
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