Question

I am stuck on a complex rational problem
solve, simplify result. leave in factored form

x-2/x+2 + x-1/x+1 / x/x+1 - 2x-3/x

Answer 1

I would start out by reciprocating it. That is multiplying the inverse of the bottom fraction by the top.
So you have:
\[((x-2/x+2) +( x-1/x+1)) * ((x/x+1)-(2x-3)/x)\]
Now you need to make common denominators for both parts of the equation.
Let's start with the left side.
((x-2)(x+1)+(x-1)(x+2))/(x+2)(x+1) is your first part.
The second part (to the right of *) is:
x^2/(x(x+1))-(2x-3)(x+1)/(x(x+1)
Now if we multiply these out, we have:
The left side is: (x^2-x-3+x^2+2x)/x^2+x+2
The right side is: (x^2+2x(x+1)+3)/(x^2+x)
if we multiply these two answers by each other, we have:
(((x-2)(x+1)+x(x+2)-1)(x^2-2x(x+1+3))/((x(x+1)+2)(x^2+x))

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