Answer:
[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]
Step-by-step explanation:
Given two expression, we have to find the difference of these two.
[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]
[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]
[tex]\text{Taking (x+2) common from the denominator }[/tex]
[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]
[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]
which is required difference.
