Question

What is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)

Answer 1

`(x+5)/(x+2) - (x+1)/(x^(2)+2x ) = (x^(2)+4x-1 )/( x^(2) +2x)`

Answer 2

`\text{The difference is }(x^2+4x-1)/(x(x+2))`

Explanation:

Given two expression, we have to find the difference of these two.

`(x+5)/(x+2)-(x+1)/(x^2+2x)`

`=(x+5)/(x+2)-(x+1)/(x(x+2))`

`\text{Taking (x+2) common from the denominator }`

`=(1)/(x+2)((x+5)-(x+1)/(x)`

`=(1)/(x+2)((x(x+5)-(x+1))/(x))`

`=(1)/(x+2)((x^2+5x-x-1)/(x)`

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

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

which is required difference.