To solve a rational inequality, we factor the numerator and the denominator into irreducible factors. The cut points are the real __________ of the numerator and the real ________ denominator. Then we find the intervals determined by the _________ ________, and we use test points to find the sign of the rational function on each interval. Let r(x)=(x+2)(x−1)(x−3)(x+4) Fill in the diagram below to find the intervals on which r(x)≥0. Sign of−4−213x+2x−1x−3x+4(x+2)(x−1)(x−3)(x+4) From the diagram we see that r(x)≥0 on the intervals _______, _______, and _______.

Question

To solve a rational inequality, we factor the numerator and the denominator into irreducible factors. The cut points are the real __________ of the numerator and the real ________ denominator. Then we find the intervals determined by the _________ ________, and we use test points to find the sign of the rational function on each interval. Let r(x)=(x+2)(x−1)(x−3)(x+4) Fill in the diagram below to find the intervals on which r(x)≥0. Sign of−4−213x+2x−1x−3x+4(x+2)(x−1)(x−3)(x+4) From the diagram we see that r(x)≥0 on the intervals _______, _______, and _______.

falhiblesw · Accepted Answer

To solve a we factor the numerator and the denominator into irreducible factors. The cut points are the real zeros of the numerator and the real zeros denominator. Then we find the intervals determined by the cut points, and we use test points to find the sign of the rational function on each interval. Let r(x)=r(x)=(x+2)(x−1)(x−3)(x+4) Set the numerator equal to zero and solve for x. (x+2)(x−1)=0 ⇒x+2=0 and x−1=0 ⇒x=−2 and x=1 Set the denominator equal to zero and solve for x. (x−3)(x+4)=0 ⇒x−3=0 and x+4=0 ⇒x=3 and x=−4 Therefore, the cut points are x=−4,x=−2,x=1 and x=3. Sign of(−∞,−4)(−4,−2)(−2,1)(1,3)(3,∞)x+2−−+++x−1−−−++x−3−−−−+x+4−++++(x+2)(x−1)(x−3)(x+4)+−+−+ From the diagram, we see that r(x)≥0 on the intervals (−∞,−4),(−2,1) and (3,∞).

To solve a rational inequality, we factor the numerator andthe denominator into

Answered question

Answer & Explanation

New Questions in Other