Question

Divide. (x^2+2x+1) /(x-2) /(x^2-1) /(x^2-4)

Answer 1

Answer: The required answer is
`(x^2+3x+2)/(x-1).`

Step-by-step explanation: We are given to divide the following algebraic expression :

`E=((x^2+2x+1)/(x-2))/((x^2-1)/(x^2-4)).`

We know that

`(a/b)/(c/d)=(a)/(b)*(d)/(c).`

So, for the given expression E, we have

`E\\\\\\=((x^2+2x+1)/(x-2))/((x^2-1)/(x^2-4))\\\\\\=(x^2+2x+1)/(x-2)*(x^2-4)/(x^2-1)\\\\\\=((x+1)^2)/((x-2))*((x+2)(x-2))/((x+1)(x-1))\\\\\\=((x+1)(x+2))/(x-1)\\\\\\=(x^2+3x+2)/(x-1).`

Thus, the required answer is
`(x^2+3x+2)/(x-1).`

Answer 2

( x² + 2 x + 1 ) / ( x - 2 ) / ( x² - 1 ) / ( x² - 4 ) =
= ( x² + 2 x + 1 )·( x² - 4 ) / ( x - 2 )·( x² - 1 ) =
= ( x + 1 )²·( x - 2 )·( x + 2 ) / ( x - 2 )·( x - 1 )·( x + 1 ) =
= ( x + 1 )·( x + 2 ) / ( x - 1 )