Question

What is the difference?

StartFraction x + 5 Over x + 2 EndFraction minus StartFraction x + 1 Over x squared + 2 x EndFraction
StartFraction x squared + 4 x minus 1 Over x (x + 2) EndFraction
StartFraction x squared + 4 x + 1 Over x (x + 2) EndFraction
StartFraction 4 Over negative 1 (x squared + x minus 2) EndFraction
StartFraction x squared + 6 x + 1 Over x (x + 2) EndFraction

Answer 1

Compute a common denominator x(x+2):

(x+5)/(x+2) - (x+1)/(x^2+2x)
= x(x+5)/[x(x+2)] - (x+1)/[x(x+2)]
= (x^2+5x - (x+1)) / [x(x+2)]
= (x^2+4x-1) / [x(x+2)].

So the difference is (x^2 + 4x - 1)/(x(x+2)), with x ≠ 0, -2.