What is (4x^2-81)/(x^2-64)<= 0 ?

The solution to (4x^2-81)/(x^2-64)<= 0 is -8<x<=-9/2 \lor 9/2 <= x<8

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(4x^2-81)/(x^2-64)<= 0

\frac{4 x ^{2} - 81}{x ^{2} - 64} \leq 0

- 8 < x \leq - \frac{9}{2} or \frac{9}{2} \leq x < 8

Solution steps

\frac{4 x ^{2} - 81}{x ^{2} - 64} \leq 0

Factor

\frac{4 x ^{2} - 81}{x ^{2} - 64} : \frac{( 2 x + 9 ) ( 2 x - 9 )}{( x + 8 ) ( x - 8 )}

\frac{( 2 x + 9 ) ( 2 x - 9 )}{( x + 8 ) ( x - 8 )} \leq 0

Identify the intervals

- 8 < x \leq - \frac{9}{2} or \frac{9}{2} \leq x < 8

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What is (4x^2-81)/(x^2-64)<= 0 ?
The solution to (4x^2-81)/(x^2-64)<= 0 is -8<x<=-9/2 \lor 9/2 <= x<8