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mathmath333
 one year ago
Find the range of \(x\).
mathmath333
 one year ago
Find the range of \(x\).

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} \dfrac{(x+3)(x^24)}{(x1)^2}\leq 0\hspace{.33em}\\~\\ \end{align}}\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Since \((x1)^2\) is always positive, Multiply both sides by that, then we are down to \((x+3)(x^24)\le0\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Then try find root of \((x+3)(x^24)=0\), then determine which intervals between roots exclusive would have \((x+3)(x^24)\) be smaller than 0

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Yeah but there are more @imqwerty

idku
 one year ago
Best ResponseYou've already chosen the best response.0at first \(x\ne1\) now, for this right side to be =0, x=2, 2, 3 for the right side to be greater than 0, (x+3) and (x^24) , both have to be negative, or both positive NOTE: (x1)^2 is always positive x+3 and (x2)(x+2) are both pos. when x>2 x+3 and (x2)(x+2) are both neg. when x<3 x>2 or x<3 and x = 2, 2, 3 CONCLUSION x\(\le\)3, or x \(\ge\) 2 and x=2

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3well if you multiply both sides of the equation by (x 1)^2 then you get \[(x + 3)(x^24) \le 0\] so this becomes \[(x + 3)(x2)(x+2) \le 0\] so the zeros are x= 3, 2 and 2 so pick some test values that are between the zeros and check dw:1433794059127:dw x = 0 you get 12/1 pick x = 2.5 you get a positive

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3so the graph would look like dw:1433794220437:dw in some way... hope it makes sense

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3now you can define the intevals where the inequality holds true.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3there is an oblique asymptote which won't affect the solution

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2x<=3 or 2<=x<1 or 1<x<=2

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Direct answer isn't allowed... @imqwerty

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3but it is good that you adjusted your answer @imqwerty after seeing some solutions

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.3but then again @imqwerty I think you solution is still incorrect... Can't see how 1 plays a roll in the solution

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.21 can't be the solution because then the denominator will become 0 @campbell_st
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