What is (n+1)/(2n-1)<= (n+2)/(2n+1) ?

The solution to (n+1)/(2n-1)<= (n+2)/(2n+1) is -1/2 <n< 1/2

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(n+1)/(2n-1)<= (n+2)/(2n+1)

\frac{n + 1}{2 n - 1} \leq \frac{n + 2}{2 n + 1}

- \frac{1}{2} < n < \frac{1}{2}

Solution steps

\frac{n + 1}{2 n - 1} \leq \frac{n + 2}{2 n + 1}

Rewrite in standard form

\frac{1}{( 2 n - 1 ) ( 2 n + 1 )} \leq 0

\frac{1}{a} \leq 0

then

a < 0

(2 n - 1) (2 n + 1) < 0

Identify the intervals

- \frac{1}{2} < n < \frac{1}{2}

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What is (n+1)/(2n-1)<= (n+2)/(2n+1) ?
The solution to (n+1)/(2n-1)<= (n+2)/(2n+1) is -1/2 <n< 1/2