Given $f(x)=\frac{x-1}{x+5}$, find all values for $x$ for which $f(x)0$.
A) $(1, \infty)$
B) $(-\infty,-5) \cup(1, \infty)$
C) $(-5,1)$
D) $(-\infty,-5)$

Question

Given $f(x)=\frac{x-1}{x+5}$, find all values for $x$ for which $f(x)>0$.
A) $(1, \infty)$
B) $(-\infty,-5) \cup(1, \infty)$
C) $(-5,1)$
D) $(-\infty,-5)$

Quizplus · Accepted Answer

The function $f(x)=\frac{x-1}{x+5}$ is positive when both the numerator and denominator are of the same sign, either both positive or both negative. This occurs in two intervals: when $x > 1$, both the numerator and denominator are positive, and when $x < -5$, both are negative. Thus, the correct intervals are $(-\infty,-5) \cup(1, \infty)$.

Given f(x)=x−1x+5f(x)=\frac{x-1}{x+5}f(x)=x+5x−1​ , Find All Values For xxx For Which f(x)>0f(x)>0f(x)>0 A) (1,∞)(1, \infty)(1,∞)

Given $f(x)=\frac{x-1}{x+5}$ , Find All Values For $x$ For Which $f(x)>0$
A) $(1, \infty)$