The denominator of a rational number
Question:

The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is——.

Solution:

$x+9$

Let numerator be $x$. Then, denominator $=x+10$

$\therefore$ Rational number $=\frac{x}{x+10}$

According to the question,

New rational number $=\frac{\text { Numerator }+1}{\text { Denominator }-1}=\frac{x+1}{x+10-1}=\frac{x+1}{x+9}$

Hence, the new denominator is $x+9$.