Change y = (x + 2)/(x + 1) into a form of y = (a)/(x + p) + q ​

Question

Change


`y = (x + 2)/(x + 1)`
into a form of

`y = (a)/(x + p) + q`
​

Answer 1

Simple manipulation of the numerator:

`(x+2)/(x+1) = ((x+1)+1)/(x+1) = (x+1)/(x+1) + \frac1{x+1}`

Then if x ≠ -1, the first term reduces to 1 :

`(x+2)/(x+1) = 1 + \frac1{x+1}`

so that a = p = q = 1.