Question

The numerator of a fraction is 2 less than the denominator. If 1 is added to both numerator and denominator the sum of the new and original fraction is 19/15. Find the original fraction.

Answer 1

SOLUTION:-

Given:

•The numerator of a fraction is 2 less than the denominator.

•1 is added to both numerator & denominator the sum of the new & original fraction is 19/15.

To find:

The fraction.

Explanation:

Let the denominator be R.

Numerator= R -2

The fraction= R-2/R

Therefore,

$= > \frac{R - 2 + 1}{R + 1} \\ \\ = > \frac{R - 1}{R + 1}$

Sum of the fraction:

$= > \frac{R - 2}{R} + \frac{R - 1}{R + 1} = \frac{19}{15}$

Taking L.C.M, we get;

$= > \frac{(R - 2)(R + 1) + R(R - 1)}{R(R+ 1)} = \frac{19}{15} \\ \\ = > \frac{ {R}^{2} + R - 2R- 2 + {R}^{2} - R }{ {R}^{2} + R} = \frac{19}{15} \\ \\ = > \frac{2 {R}^{2} - 2R - 2}{ {R}^{2} +R } = \frac{19}{15} \\ [cross \: multiplication] \\ = > 30 {R}^{2} - 30R - 30 = 19 {R}^{2} + 19R\\ \\ = > 30 {R}^{2} - 19 {R}^{2} - 30R - 19R - 30 = 0 \\ \\ = > 11 {R}^{2} - 49R - 30 = 0 \\ \\ = > 11 {R}^{2} - (55R - 6R) - 30 = 0 \\ \\ = > 11 {R}^{2} - 55R + 6R - 30 = 0 \\ \\ = > 11R(R - 5) + 6(R - 5) = 0 \\ \\ = > (R - 5)(11R + 6) = 0 \\ \\ = > R - 5 = 0 \: \: or \: \: 11R+ 6 = 0 \\ \\ = > R = 5 \: \: \: or \: \: \: \: 11R = - 6 \\ \\ = > R = 5 \: \: \: or \: \: \: R = - \frac{6}{11}$

So, the value of R= -6/11 is not acceptable because it's negative.

Therefore,

R =5

The fraction;

$= > \frac{R - 2}{R} \\ \\ = > \frac{5 - 2}{5} \\ \\ = > \frac{3}{5}$

Thus,

The fraction is 3/5.

:)

Answer 2

Answer:

Step-by-step explanation:

Check of the answer is 3/5+10/15 19/15