Solving Rational Expressions - RQD HALP

Hay /sci/.

I've been trying to do this question for well over 2 hours. My friends have tried to help me, but I rejected them, believing I could do it myself. I do realize that the majority of users here are of a college/university math level...so I hope you can understand that we were all once fucking confused and help me out here.

Solve.

x+2 / x-1 + x-4 / x+2 =  x+1/x-1 + 1/2

I have the answer, but I don't know how to solve it. Thanks.

ive never seen anyone refer to csc(x) as sin^-1(x), sometimes sin(x)^-1, which is consistent and makes sense.

f^-1(x) != f(x)^-1
theyre two separate concepts, if you see them used interchangably its because whoever is presenting them doesn't understand what the notation means.

i agree that writing sin x is being loose though, and most teachers who pay attention will use parentheses because they recognize that it is a function.

to illustrate the inequality
suppose f(x) = x + 3
f^-1(x) = x - 3
satisfies f^-1(f(x)) = x

f(x)^1 = 1/(x+3)
satisfies f(x)*(f(x)^-1) = 1