Solve the rational inequality. Express the solution in interval notation.
-$ \frac{x-5}{x+1}0 $
A) $( 5 , \infty )$
B) $( - 1,5 )$
C) $( - \infty , - 1 )$
D) $( - \infty , - 1 ) \cup ( 5 , \infty )$

Question

Solve the rational inequality. Express the solution in interval notation.
-$ \frac{x-5}{x+1}>0 $
A) $( 5 , \infty )$
B) $( - 1,5 )$
C) $( - \infty , - 1 )$
D) $( - \infty , - 1 ) \cup ( 5 , \infty )$

Quizplus · Accepted Answer

The inequality $ \frac{x-5}{x+1}>0 $ is satisfied when the numerator and denominator have the same sign (both positive or both negative). The critical points are $x = 5$ (numerator equals zero) and $x = -1$ (denominator equals zero). Testing intervals around these points shows that the inequality is satisfied for $x < -1$ and $x > 5$, leading to the solution $( - \infty , - 1 ) \cup ( 5 , \infty )$.

Solve the Rational Inequality x−5x+1>0 \frac{x-5}{x+1}>0 x+1x−5​>0 A) (5,∞)( 5 , \infty )(5,∞)

Solve the Rational Inequality $\frac{x-5}{x+1}>0$ A) $( 5 , \infty )$