What is (25x^2-81)/(x^2-36)<= 0 ?

The solution to (25x^2-81)/(x^2-36)<= 0 is -6<x<=-9/5 \lor 9/5 <= x<6

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(25x^2-81)/(x^2-36)<= 0

\frac{25 x ^{2} - 81}{x ^{2} - 36} \leq 0

- 6 < x \leq - \frac{9}{5} or \frac{9}{5} \leq x < 6

Interval Notation

(- 6, - \frac{9}{5}] \cup [\frac{9}{5}, 6)

Decimal Notation

- 6 < x \leq - 1.8 or 1.8 \leq x < 6

Solution steps

\frac{25 x ^{2} - 81}{x ^{2} - 36} \leq 0

Factor

\frac{25 x ^{2} - 81}{x ^{2} - 36} : \frac{( 5 x + 9 ) ( 5 x - 9 )}{( x + 6 ) ( x - 6 )}

\frac{( 5 x + 9 ) ( 5 x - 9 )}{( x + 6 ) ( x - 6 )} \leq 0

Identify the intervals

- 6 < x \leq - \frac{9}{5} or \frac{9}{5} \leq x < 6

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3 z^{2} + 12 z - 20 = 5 z

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r^{2} - 3 r - 40 = 0

What is (25x^2-81)/(x^2-36)<= 0 ?
The solution to (25x^2-81)/(x^2-36)<= 0 is -6<x<=-9/5 \lor 9/5 <= x<6