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Write a math paper quickly.
1.(a-2b)/b =(a+b-3b)/b =(a+b)/b-3 = 5/3

So (a+b)/b = 14/3.

2. Take x=a/(b+c)=b/(a+c)=c/(b+a) as the reciprocal.

Then both sides of (b+c)/a = (a+c)/b are multiplied by ab.

That is, a+b = -c or a = b.

Similarly, b+c = -a or b = C.

C+a = -b or a = c

So x =-1 or 1/2.

3.AB:PB =(AP+BP):BP = AP:BP+ 1 = 8:5

You can also set each copy to x, so AP = 3x BP =5x.

That is AB = 8x.

So AB:BP = 8:5