Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 8 } { ( x + 4 ) ^ { 2 } }

Question

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$$
A) $( - \infty , - 4 )$
B) $\varnothing$
C) $( - 4,0 )$
D) $( - \infty , \infty )$

Quizplus · Accepted Answer

The expression $\frac { 8 } { ( x + 4 ) ^ { 2 } }$ is always positive for any real value of $x$ because the numerator is positive and the square of any real number (including $x + 4$) is also positive. Therefore, the inequality $\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$ has no solution, as the expression cannot be less than 0 for any real value of $x$.

Solve the Rational Inequality 8(x+4)2<0\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0(x+4)28​<0

Solve the Rational Inequality $\frac { 8 } { ( x + 4 ) ^ { 2 } } < 0$