A fraction

I think of a fraction, if we increase its numerator and denominator by one, the value of the fraction increases by one tenth, what fraction do I think?

Correct answer:

x =  2/5

Step-by-step explanation:

a/b=x b+1a+1=101+ba (a+1)/(b+1)=1/10+a/b (a+1)/(b+1)=10bb+10a  a=2 10ab2+9b=0  10 2b2+9 b=0 b2+9b20=0 b29b+20=0  p=1;q=9;r=20 D=q24pr=924120=1 D>0  b1,2=2pq±D=29±1 b1,2=29±1 b1,2=4.5±0.5 b1=5 b2=4   Factored form of the equation:  (b5)(b4)=0  b=b1=5  x=a/b=2/5=52=0.4=52=0.4   Verifying Solution:   r1=4+12+1101=21=0.5 r2=5+12+1101=52=0.4

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