Question 306988
Imaginary, what do you mean? 
You can solve algebraically or by graphing.
{{{drawing(300,300,-10,8,-8,8,blue(line(-1,-10,-1,10)),blue(line(-4,-10,-4,10)), graph( 300, 300, -10, 8, -8,8, (x+3)/(x+1), 2/(x+4))) }}}
f(x) is the red function.
g(x) is the green function.
You can clearly make out that between (-4,-1) that f(x) is less than g(x). 
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Now let's show it algebraically.
Both function have singularities. 
f(x) at x=-1 and g(x) at x=-4.
Break up the number line into three regions and check the inequality in those regions. You can pick any point in the region just not the end points. 
1:({{{-infinity}}},{{{-4}}})
2:({{{-4}}},{{{-1}}})
3:({{{-1}}},{{{infinity}}})
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Region 1: Let x=-5.
{{{(x+3)/(x+1)<2/(x+4)}}}
{{{(-5+3)/(-5+1)<2/(-5+4)}}}
{{{(-2)/(-4)<-2}}}
{{{1/2<-2}}}
No, not a valid region.
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Region 2: Let x=-2.
{{{(x+3)/(x+1)<2/(x+4)}}}
{{{(-2+3)/(-2+1)<2/(-2+4)}}}
{{{(1)/(-1)<2/(2)}}}
{{{-1<1}}}
Yes, a valid region.
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Region 3: Let x=0.
{{{(x+3)/(x+1)<2/(x+4)}}}
{{{(3)/(1)<2/(4)}}}
{{{3<1/2}}}
No, not a valid region.