Question

The denominator of a rational number is greater than its numerator by 4. If the numerator is increased by 7 and the denominator is decreased by 2, the new number becomes 6/5. Find the original rational number.​

Answer 1

$\huge\mathfrak\pink{A N S W E R}$

Let the denominator be 'x'

Then, the numerator = x + 4

$\small\mathfrak\pink{the \: number \: } \: = \: \frac{x \: + \: 4}{x}$

$Condition 1 = \frac{x + 4 - 7}{x - 2} \\ </strong></h3><h3><strong>[tex]Condition 1 = \frac{x + 4 - 7}{x - 2} \\ Condition 2 = \frac{x + 4 - 7}{x - 2} = \frac{6}{5}$

According to the conditions:-

$\frac{x + 4 - 7}{x - 2} = \frac{6}{5}$

$\frac{x - 3}{x - 2} = \frac{6}{5}$

5(x - 3) = 6(x - 2)

5x - 15 = 6x - 12

5x - 6x = -12 + 15

-x = 3

$x = \frac{ 3}{ - 1} \\ x = - 3$

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