What is (x^2-25)/(3x-6)<= 0 ?

The solution to (x^2-25)/(3x-6)<= 0 is x<=-5\lor 2<x<= 5

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(x^2-25)/(3x-6)<= 0

\frac{x ^{2} - 25}{3 x - 6} \leq 0

x \leq - 5 or 2 < x \leq 5

Interval Notation

(- \infty, - 5] \cup (2, 5]

Solution steps

\frac{x ^{2} - 25}{3 x - 6} \leq 0

Factor

\frac{x ^{2} - 25}{3 x - 6} : \frac{( x + 5 ) ( x - 5 )}{3 ( x - 2 )}

\frac{( x + 5 ) ( x - 5 )}{3 ( x - 2 )} \leq 0

Multiply both sides by

3

\frac{3 ( x + 5 ) ( x - 5 )}{3 ( x - 2 )} \leq 0 \cdot 3

Simplify

\frac{( x + 5 ) ( x - 5 )}{x - 2} \leq 0

Identify the intervals

x \leq - 5 or 2 < x \leq 5

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4 x - 4 = 3 x + 3

\frac{3 - i}{1 + i}

What is (x^2-25)/(3x-6)<= 0 ?
The solution to (x^2-25)/(3x-6)<= 0 is x<=-5\lor 2<x<= 5