# SOLUTION: x^2+3x/x^2-36 less than or equal to 0 It says solve the inequality

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 Question 727814: x^2+3x/x^2-36 less than or equal to 0 It says solve the inequality Answer by stanbon(60771)   (Show Source): You can put this solution on YOUR website!It says solve the inequality ------------- (x^2+3x)/(x^2-36) <= 0 ======== Factor: (x(x+3))/[(x-6)(x+6)] <= 0 ----- Critical value are x = -6,-3,0,6 ------ Draw a number line and plot those x values The equality is true for x = 0 and for x = -3 -------------------------- Test the inequality for a value in each of the 5 intervals defined by those x values. ------------------- (x(x+3))/[(x-6)(x+6)] <= 0 Test x = -10:: -*-/-*- <= 0 ; false Test x = -5::: -*-/-*+ <= 0 ; true Test x = -1::: -*+/-*+ <= 0 ; false Test x = 3:::: +*+/-*+ <= 0 ; true Test x = 10::: +*+/+*+ <= 0 ; false ----- Solutions: (-6,-3]U[0,6) ================================ Cheers, Stan H.