Determine which numbers should be removed from the domain and Solve the equation

Question

#1. 1/x+2 + 4/x² -4=1

#2. x/x+2 + 5/x-2 = 20/x²-4

Answer 1

#2 x cannot = 2 or -2 as that would make division by zero in one of the 3 fractions

multiply both sides of the equation by x^2-4 to remove the fractions

x(x-2) + 5(x+2) = 20

x^2 -2x +5x +10 =20

x^2 +3x -10 = 0

factor

(x-2)(x+5) = 0

x =-5, ignore x=2 as it would make the original equation involve division by zero

x=-5 is the only solution

#1 is the same as to the domain x cannot equal 2 or -2

1/x+2 +4/x^2-4 =5

multiply both sides by x^2-4

x-2 + 4 = 5x^2-20

5x^2 -x -22 = 0

factor

(5x -11)(x+2) = 0

5x-11 =0

5x = 11

x =11/5 is the only solution