What is the quotient 6-x/x^2 + 2x - 3 divided by x^2 - 4x - 12/x^2+4x+3 in simplified form? State any restrictions on the variable

Question

anonymous · Answer

I know the answer already is -(x+1)/(x-1)(x+2)

anonymous · Answer

how do I find the variables?

luigi0210 · Answer

Do you know how to start off?

ashleyisakitty · Answer

@Luigi0210 how do i do this one? :P

luigi0210 · Answer

change the division to multiplication and flip the second

luigi0210 · Answer

Do you need me to do it to show you?

ashleyisakitty · Answer

Yes, that would be most helpful to go by steps :)

luigi0210 · Answer

Okay so we have this:
$$\frac{6-x}{x^2+2x-3}\div\frac{x^2-4x-12}{x^2+4x+3}$$
So now you change the signs and flip the equation around:
$$\frac{6-x}{x^2+2x-3}*\frac{x^2+4x+3}{x^2-4x-12}$$
So now start factoring what you can:
$$\frac{-(x-6)}{(x+3)(x-1)}*\frac{(x+3)(x+1)}{(x-6)(x+2)}$$

Do you know what to do now Miss Ashley?

ashleyisakitty · Answer

yes! thank you!

luigi0210 · Answer

Anytime :)