Question

The denominator of a rational number is greater than
its numerator by 8. If the numerator is increased by
17 and the denominator is decreased by 1, the
number obtained is 3/2. Find the rational number.​

Answer 1

Step-by-step explanation:

hope it helps u........

Answer 2

${ \huge{ \pink{ \underline{ \underline{ \red{ \mathbb{ \bigstar{ \purple{answer}}}}}}}}} \\ \bf \: let \: the \: numerator \: of \: rational \: number \: = \: x \: \\ \sf \: then \: denominator \: of \: rational \: number \: = x + 8 \\ \sf \: the \: rational \: number \: = \frac{x}{x + 8} \\ \bf \: using \: the \: given \: information \: \\ \sf \: \frac{x + 17}{(x + 8) - 1} = \frac{3}{2} = > \frac{x + 17}{x + 7} = \frac{3}{2} \\ = > 2(x + 17) = 3(x + 7) \: { \green{ \mathbb{by \: cross \: multiplication}}} \\ = > 2x + 34 = 3x + 21 = > 2x - 3x = 21 - 34 \\ = > - x = - 13 \: = > x = 13 \\ { \red{ \mathbb{putting \: the \: real \: value \: of \: x \: }}} \\ hence \: the \: required \: rational \: number \: is : \\ \frac{x}{x + 8} = > \frac{13}{13 + 8} = > \frac{13}{21} \\ \\ answer = > \frac{13}{21}$