The difference between the two given fractions is [tex]\frac{x^{2} +4x-1}{x^{2} +2x}[/tex].
Fraction if a part of whole. It is represented in the form of numerator and denominator.
Given that,
[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]
Take the LCM of the denominators is [tex]x(x+2)[/tex].
= [tex]\frac{x(x+5)-(x+1)}{x(x+2)}[/tex]
= [tex]\frac{x^{2}+5x -x-1}{x^{2} +2x}[/tex]
= [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex]
Thus, the difference between the two given fractions is [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex] .
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