Solve the inequality. Write the solution set in interval notation.
-$\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } 0$
A)(-3, 2)U(2, 3)
B)(-?, -3)U(3, ?)
C)(-?, -3)U(2, 3)
D)(-3, 2)U(3, ?)

Question

Solve the inequality. Write the solution set in interval notation.
-$\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0$
A)(-3, 2)U(2, 3)
B)(-?, -3)U(3, ?)
C)(-?, -3)U(2, 3)
D)(-3, 2)U(3, ?)

Quizplus · Accepted Answer

The inequality $\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0$ is positive when the numerator and denominator have the same sign and the denominator is not zero. The denominator $x^2 - 9 = (x-3)(x+3)$ is zero at $x = 3$ and $x = -3$, so these are the critical points. The numerator $(x-2)^2$ is always non-negative. The solution set is all x except where the expression is undefined or zero, which excludes $x = 3$ and $x = -3$, leading to the intervals $(-∞, -3) \cup (3, ∞)$.

Solve the Inequality (x−2)2x2−9>0\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0x2−9(x−2)2​>0

Solve the Inequality $\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0$