Question

the denominator of a rational number is greater than its numerator by 5. if the numerator is increased by 7 and denominator decrease by 4, the number obtained is 5/3. find the rational number​

Answer 1

Step-by-step explanation:

$\frac{x - 5 + 7}{x - 4} = \frac{5}{3} \\ 3x + 6 = 5x - 20 \\ 5x - 3x = 6 + 20 \\ 2x = 26 \\ x = 13$

fraction/ Ans : 8/13

Answer 2

Answer:

The rational number is $\frac{8}{13}$

Step-by-step explanation:

Let x be the numerator and x + 5 be the denominator.

⇒ $\frac{(x)+7}{(x+5)-4} = \frac{5}{3}$

⇒ x + 7 = $\frac{5}{3}$ ×$\frac{(x+5)- 4}{1}$

⇒ x + 7 = $\frac{5x + 25 - 20 }{3}$

⇒ x + 7 = $\frac{5x + 5}{3}$

⇒ 3(x + 7) = 5x + 5

⇒ 3x + 21 = 5x + 5

⇒ 5x - 3x = 21 - 5

⇒ 2x = 16

⇒ x = 8

Thus, the numerator is 8 and the denominator is 13. The rational number is $\frac{8}{13}$

I hope this helps!!