Question

The numerator of a rational number is 7 less than the denominator. if the denominator is increased by 7 and the numerator by 2, we get the same rational number.find the rational number.

Answer 1

Answer:

The rational number is $\frac{2}{7}$.

Step-by-step explanation:

Let the rational number be, $\frac{x}{y}$.

it is provided that, x = y - 7.

$\frac{y-7}{y}=\frac{y-7+2}{y+7}\\\frac{y-7}{y}=\frac{y-5}{y+7}\\(y-7)(y+7)=y(y-5)\\y^{2}-49=y^{2}-5y\\5y=49\\y=\frac{49}{5}$

The value of x is:

$x=y-7\\=\frac{49}{5}-7\\=\frac{49-35}{5}\\=\frac{14}{5}$

The rational number is:

$\frac{x}{y} =\frac{14/5}{49/5}=\frac{14}{49}=\frac{2}{7}$

Thus, the rational number is $\frac{2}{7}$.