Question

The numerator of fraction is 3 less than the denominator . If 2 is added both the numerator and denominator then the sum of new fraction and the original fraction is 29/20.Find the original fraction.

Answer 1

Answer:

The fraction is 7/10.

Step-by-step explanation:

let denominator be x

so numerator be x-3

fraction=x-3/x

when 2 is added both up and down then fraction=x-1/x+2

according to the question

(x-3/x)+(x-1/x+2) =29/20

11x^2-98x-120=0

then buy middle term split

x=10,-12/11

so,the fraction is 7/10

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Denominator be p

Numerator be p - 3

Now,

Fraction becomes = p - 3/p

Situation,

(p - 3) + 2/p + 2 + (p - 3)/p = 29/20

(p - 1)/(p + 2) + (p - 3)/p = 29/20

p(p - 1) + (p - 3) (p + 2)/p(p + 2) = 29/20

(p² - p) + (p² - p - 6)/p² + 2p = 29/20

20(2p² - 2p - 6) = 29(p² + 2p)

40p² - 40p - 120 = 29p² + 58p

11p² - 98p - 120 = 0

Now,

Splitting middle term,

11p² - 110p + 12p - 120 = 0

11p(p - 10) + 12(p - 10) = 0

(p - 10)(11p + 12) = 0

p - 10 = 0 or 11p + 12 = 0

p = 10, -12/11 (Negative value is not acceptable)

p = 10

Denominator = p = 10

Numerator

= p - 3

= 10 - 3

= 7

Fraction = 7/10