Question

Solve the inequality​

Answer 1

Answer:

n=(-7,-3)

Step-by-step explanation:

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Answer 2

Answer:

x<−12+−12√5 or 0<x<−12+12

Step-by-step explanation:

Let's solve your inequality step-by-step.

x−1x+3<2

x2+3x−1x<2

Let's find the critical points of the inequality.

x2+3x−1x=2

x2+3x−1=2x(Multiply both sides by x)

x2+3x−1−2x=2x−2x(Subtract 2x from both sides)

x2+x−1=0

For this equation: a=1, b=1, c=-1

1x2+1x+−1=0

x=−b±√b2−4ac2a(Use quadratic formula with a=1, b=1, c=-1)

x=−(1)±√(1)2−4(1)(−1)2(1)

x=−1±√52

x=−12+12√5 or x=−12+−12√5

Check possible critical points.

x=−12+12√5(Works in original equation)

x=−12+−12√5(Works in original equation)

Critical points:

x=−12+12√5 or x=−12+−12√5(Makes both sides equal)

x=0(Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<−12+−12√5(Works in original inequality)

−12+−12√5<x<0(Doesn't work in original inequality)

0<x<−12+12√5(Works in original inequality)

x>−12+12√5(Doesn't work in original inequality)