Question

x-3/×+3 + x+3/x-3 = 2 1/2 solved it by factorization method.​

Answer 1

Step-by-step explanation:

Considering x-3=a

x+3=b

a/b+b/a=5/2

a^2+b^2/ab=5/2

2a^2+2b^2=5ab

2(x-3)^2+2(x+3)^2=5(x-3)(x+3)

2(x^2+9-6x)+2(×^2+9+6x)=5(x^2-9)

2x^2-12x+18+2x^2+12x+18=5x^2-45

4x^2+36=5x^2-45

x^2-81=0

x^2-9^2=0

It is in the form a^2-b^2=(a+b)(a-b)

(x+9)(x-9)=0

x=-9,9