Question

Solve the following quadratic equations by factorization:  

`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`

 

Answer 1

`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`

 ⟹ `((x-3)^2+(x+3)^2)/((x+3)(x-3))=5/2` 

⟹ `(x^2-6x+9+x^2+6x+9)/(x^2-9)=5/2` 

⟹ `2(2x^2 + 18) = 5(x^2 – 9)`
⟹ `4x^2 + 36 = 5x2 – 45`
⟹ `x^2 – 81 = 0`
⟹ `x^2 – 9^2 = 0`
⟹ `(x + 9) (x – 9) = 0` 

If x + 9 = 0  Or  x – 9 = 0
Then x = − 9  Or  x = 9