Prove monotonicity of function by definition

Specific steps:

(1) takes any two values.

(2) Doing errands

(3) Deformation (factorization, formula, physicalization, etc. )

(4) number

(5) draw a conclusion

Prove:

Let x 1, x2 ∈ (- 1, +∞), x 1 < x2.

Then f (x 1)-f (x2)

=a^(x 1)+[(x 1-2)/(x 1+ 1)]-a^(x2)+[(x2-2)/(x2+ 1)]

=[a^(x 1)-a^(x2)]+[[(x 1-2)(x2+ 1)-(x2-2)(x 1+ 1)]/(x 1+ 1)(x2+ 1)]

=[a^(x 1)-a^(x2)]+[ 3(x 1-x2)/(x 1+ 1)(x2+ 1)]

∵ y = a x (a > 1) is the increasing function in the definition.

∴a^x 1