Solve the inequality.
-$$\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 }

Question

Solve the inequality.
-$$\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 } < 0$$
A) $( - \infty , - 6 ) \cup ( - 5 , - 1 ) \cup ( 3 , \infty )$
B) $( - 1,3 )$
C) $( - 6 , - 5 ) \cup ( - 1,3 )$
D) $( - \infty , - 3 ) \cup ( 1,3 ) \cup ( 4 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 } < 0$, factor both the numerator and the denominator. The numerator factors to $(x-3)(x+1)$ and the denominator factors to $(x+6)(x+5)$. The critical points, where the expression changes sign, are at $x = -6, -5, -1,$ and $3$. Testing intervals around these points, we find that the expression is negative between $(-6, -5)$ and $(-1, 3)$, which corresponds to choice C.

Solve the Inequality x2−2x−3x2+11x+30<0\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 } < 0x2+11x+30x2−2x−3​<0

Solve the Inequality $\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 } < 0$