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 $x+9$.