Question

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

Answer 1

Explanation:

x² + 2x = x(x + 2)

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

LCM = x(x+2)

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