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on the question i wrote on the picture, i must multiply by (x-2)² not x-2
i want to know why?

Who said you have to multiply (x-2)^2. Whats the original problem

the book
because apparently i will lose a solution if i dont

Whats the original problem

|dw:1350339676275:dw|

And your book says the solution needs to multiply both sides by (x-2)^2? in the back of the book?

yes because if i only multiply by x-2 i lose a solution
i dont see how

Hm, If you do the math the same answer comes out. Does it give you an answer to the problem

|dw:1350340054622:dw|

you have to keep in mind that x-2 could be negative, so you need to consider cases

thank you very much people!

welcome!