How do solve #(x(4-x))/(x+2)>=0# graphically?

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Answer 1 · 2017-07-06T09:44:15

The solution is #x in (-oo,-2) uu [0, 4]#

First, plot the graph

graph{(x(4-x))/(x+2) [-18.02, 18.04, -9.01, 9.01]}

The function is

#(x(4-x))/(x+2)>=0#

And look where the function is #>=0#

The solution is

#x in (-oo,-2) uu [0, 4]#