Question

the numerator of the fraction is 3 less than its denominator if 2 is added to both numerator and denominator the sum of the new fraction and the original fraction is 29/30​

Answer 1

it's very easy vaishu

let the denominator be X therefore the numerator =X-3

now adding 2 to both we get

$\binom{x - 3 + 2}{x + 2} = \binom{x - 1}{x + 2}$

now there sum =

$\binom{x - 3}{x} + \binom{x - 1}{x + 2} = \binom{29}{30}$

taking LCM WE GET

X²-X-6+X²-X. 29
—————— = ----
X²+2x. 30

(2X²-6)30=29(X²+2X)
60X²-180=29X²+58X
60X²-29X²=58X+180
31X²-58X-180=0

Now mid term splitting then you will get your answer