SOLUTION: Please show me step by the step on finding the range f(x)= (x+2)/(x^2-1) f(x) = x+2 _______ x²-1

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Question 1157066: Please show me step by the step on finding the range
f(x)= (x+2)/(x^2-1)
f(x) = x+2
_______
x²-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The range is the set of y for which the discriminant is greater or equal to zero.

find discriminant b%5E2-4ac:
y=%28x%2B2%29%2F%28x%5E2-1+%29+.....both sides multiply by %28x%5E2-1+%29+
x%2B2=y+%28x%5E2-1+%29+
x%2B2=yx%5E2-y
yx%5E2-y-x-2=0
yx%5E2-x-%28y%2B2%29=0
coefficients: a=y,b=-1,c=-%28y%2B2%29

then discriminant is:
%28-1%29%5E2-4y%28-%28y%2B2%29%29%3E=0
1-4y%28-y-2%29%3E=0
1%2B4y%5E2%2B8y%3E=0
4y%5E2%2B8y%2B1%3E=0++.....use quadratic formula
y=%28-8%2B-sqrt%288%5E2-4%2A4%2A1%29%29%2F%282%2A4%29
y=%28-8%2B-sqrt%2864-16%29%29%2F8
y=%28-8%2B-sqrt%2848%29%29%2F8
y=%28-8%2B-4sqrt%283%29%29%2F8
y=%28-1%2B-sqrt%283%29%2F2%29

Solution:
y%3C=-1-sqrt%283%29%2F2 or y%3E=-1%2Bsqrt%283%29%2F2

Interval Notation: (-+infinity+ ,-1-sqrt%283%29%2F2] U [-1%2Bsqrt%283%29%2F2, infinity )