Question

The denominator of a rational number is 5 more than its numerator. If the denominator is decreased by 2, and the numerator is decreased by 2, the number obtained by 5/7. Find the rational number​

Answer 1

Answer:

$\frac{ \frac{ - 36}{17} }{ \frac{49}{17} }$

Step-by-step explanation:

Consider Numerator = n

then, denominator = n+5

According to question

$\frac{n - 2}{(n + 5) - 2} = \frac{5}{7}$

$\frac{n - 2}{ - 2n - 10} = \frac{5}{7}$

After doing cross multiplication

$7( n - 2) = 5( - 2n - 10)$

$7n - 14 = - 10n - 50$

$10n + 7n = - 50 + 14$

$17n = - 36$

$n = \frac{ - 36}{17}$

The rational no. =

$\frac{ (\frac{ - 36}{17}) }{( \frac{ - 36}{17} + 5) } = \frac{ \frac{ - 36}{17} }{ \frac{49}{17} }$