Question

What is the difference? \frac{x+5}{x+2}-\frac{x+1}{x^{2}+2x}

Answer 1

Answer:

Step-by-step explanation:

x² + 2x = x(x + 2)

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

LCM = x(x+2)

                        $\sf =\dfrac{(x+5)*x}{(x+2)*x}-\dfrac{x+1}{x(x+2)}\\\\=\dfrac{x*x + 5*x}{x^2+2x}-\dfrac{x+1}{x^2+2x}\\\\=\dfrac{x^2+5x - (x+1)}{x^2+2}\\\\=\dfrac{x^2+5x -x - 1}{x^2+2x)}\\\\=\dfrac{x^2+4x-1}{x^2+2x}$