For what values of the variable x is the expression ((4/(x+3))-(2/(x^2-3x+2)))/((3/(x-1))+(1/(x^2+2x-3))) undefined?

Question

anonymous · Answer

what does that mean?

agreene · Answer

The expanded form is
$$\frac{4 x^2-14 x+2}{3 x^2+4 x-20}$$
Looking for when the denominator =0 will give you when it is undefined
$$3 x^2+4 x-20=0$$
solutions being:
$$x=2;-\frac{10}{3}$$

anonymous · Answer

how do you get the expanded form?

agreene · Answer

(4/(3+x)-2/(2-3 x+x^2))/(3/(-1+x)+1/(-3+2 x+x^2))
= (4/(3+x)-2/(2-3 x+x^2))/(3/(-1+x)+1/(-3+2 x+x^2))
= (4/(3+x)-2/(2-3 x+x^2))/(3/(-1+x)+1/(-3+2 x+x^2))

Algebra and junk.

agreene · Answer

not sure why that posted like that... but yeah

anonymous · Answer

so you just multiply the reciprocal?

agreene · Answer

well, you have division of division--so if you prefer to evaluated it like that then you can--I just look at it and do all the division + combine like terms.

anonymous · Answer

well i have to learn to show my work. i do the same thing the teach expects us to show all of our work but im not sure how to show it from the form they gave us to the expanded form.

anonymous · Answer

also do i search for the restrictions before starting all the work and after or just after?