Question

simplify and find restrictions.
x+1/x^2+2x-8 - x/4x-8

Answer 1

\[\frac{ x+1 }{ x^2+2x-8}-\frac{ x }{ 4x-8 }\]

Answer 2

the problem is,
=(x+1)/(x^2+2x-8)-x/(4x-8)
=(x+1)/[(x+4)(x-2)]-x/2(x-4)
=[2(x+1)(x-4)-x(x+4)(x-2)]/[(x+4)(x-2)(x+4)]
=(2x^2-6x-8-x^3-2x^2+8x)/[(x+4)(x-4)(x-2)]
=(-x^3+2x-8)/[(x+4)(x-4)(x-2)]
the restriction is the denominator should not be zero, i.e. x should not be +4,-4,+2