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Question
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 the and denominator is decreased by 1, then expression for new denominator is ______.
Solution
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 the and denominator is decreased by 1, then expression for new denominator is x + 9.
Explanation:
Let numerator be x.
Then, denominator = x + 10
∴ Rational number = `x/(x + 10)`
According to the question,
New rational number = `("Numerator" + 1)/("Denominator" - 1)`
= `(x + 1)/(x + 10 - 1)`
= `(x + 1)/(x + 9)`
Hence, the new denominator is x + 9.
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