If P = 96/ (95 × 97), Q = 97/ (96 × 98) and R = 1/97, then which of the following is TRUE?
R < Q < P
Rewrite using \((n-1)(n+1)=n^2-1\): \(P=\tfrac{96}{96^2-1}\), \(Q=\tfrac{97}{97^2-1}\).
P vs Q: The function \(f(x)=\tfrac{x}{x^2-1}\) decreases for \(x>1\), so \(P>Q\).
Q vs R: \(Q=\tfrac{97}{97^2-1}>\tfrac{97}{97^2}=\tfrac{1}{97}=R\).
Therefore R < Q < P.
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Column I
Column II
a.
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i.
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b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
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iii.
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d.
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iv.
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