Question

What is the restriction on the product of quantity x squared plus 5 x plus 4 divided by quantity x squared plus 3 x minus 4 multiplied by quantity x squared plus 4 x minus 5 divided by quantity x plus 3?

Answer 1

Well,
this is what i read :
R(x) = [(x^2 + 5x + 4) / (x^2 + 3x -4)] . (x^2 + 4x - 5)/(x + 3)
now, we have :
x^2 + 5x + 4 = (x+1)(x+4) --> check by developing...
x^2 + 3x - 4 = (x-1)(x+4)
and second factor :
x^2 + 4x - 5 = (x-1)(x+5)
therefore :

R(x) = [ (x+1)(x+4) / [(x-1)(x+4)] ] . [ (x-1)(x+5) / (x+3) ]
R(x) = [ (x+1) / (x-1) ] . [ (x-1)(x+5) / (x+3) ]
R(x) = (x+1) . (x+5) / (x+3)
finally :

in terms of restrictions, we can say that :

-----> R(x) is defined on : R \ { -3 }

hope it' ll help !!