Question

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

Answer 1

Let the of the fraction be
then the denominator of the fraction =x+3
and the fraction is
$\frac{x}{x + 3}$
If 2 is added to both the numerator and denominator, then
the fraction=
$\frac{x + 2}{ x + 3 + 2}$
A/Q
$\frac{x + 2}{x + 5} + \frac{x}{x + 3} = \frac{29}{30}$
$\frac{x + 2}{x + 5} = \frac{29}{30} - \frac{ x}{ x + 3}$
$\frac{x + 2}{x + 5} = \frac{29( x + 3) -x(30) }{30(x + 3)}$
$\frac{x + 2}{x + 5} = \frac{29x + 87 - 30x}{30x + 90}$
$\frac{ x+ 2}{ x + 5} = \frac{ - 1x + 87}{30x + 90}$
(x+2)(30x+90)=(x+5)(-1x+87)
x(30x+90)+2(30x+90)=x(-1x+87)+5(-1x+87)
$30 {x}^{2} + 90x + 60x + 180 = - 1 {x}^{2} + 87x - 5x + 435$