Question

What is the difference?

Answer 1

Answer:

$\frac{x^2+4x-1}{x(x+2)}$

Step-by-step explanation:

Given

$\frac{x+5}{x+2}$ - $\frac{x+1}{x^2+2x}$ ← factor denominator

= $\frac{x+5}{x+2}$ - $\frac{x+1}{x(x+2)}$

We require the fractions to have a common denominator.

Multiply numerator/denominator of first fraction by x

= $\frac{x(x+5)}{x(x+2)}$ - $\frac{x+1}{x(x+2)}$

Subtract terms on numerator leaving the common denominator

= $\frac{x^2+5x-x-1}{x(x+2)}$

= $\frac{x^2+4x-1}{x(x+2)}$