I need a step by step because Im missing something in my cal

I need a step by step because I\'m missing something in my calcualation and can\'t see what.

1)Solve the following inequality. Be sure to show your work using a sign chart and test values. Write your final answer in interval notation.

x^2+8x+16/x-4 less than equal to 0

2) In the following picture, assume O is at the origin (0; 0) and P is the point (4; 3) on the cartesian coordinate plane. Find the equation of the tangent line L which passes through P.

Solution

(x^2+8x+16) / (x-4) < = 0

( x+4)(x+4) / ( x- 4 ) < = 0

critical points of the inequality are

x = -4 , 4

dividing the number line into 3 intervals

----------- - 4 -------------- 4 -------------------

1st interval ( - inf , - 4) taking test point as -5

( x+4)(x+4) / ( x- 4 ) < = 0

( -5 + 4) ( -5 + 4) / ( -5 -4 ) < = 0

+ / - = negative

hence , interval is true

2nd interval ( -4 to 4 ) test point 0

( 0+4)(0+4) / ( 0- 4 ) < = 0

true

3rd interval ( 4 to + inf ) , test point 5

( 5+4)(5+4) / ( 5- 4 ) < = 0

false

solution

( - inf , 4 )