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
A: -(x+1)/(x-1)(x+2) x does not equal -3, -2, 1, and 6
B: -1/(x+2) x does not equal -3, -2, and 6
C: -(x+1)/(x-1)(x+2) x does not equal -2 and 1
D: -1/(x+2) x does not equal -2
I'm pretty sure it is either A or C
(6-x)/(x^2+2x-3)
--------------------
(x^2-4x-12)/(x^2+4x+3)
(6-x)/(x+3)(x-1)
-----------------------------
(x-6)(x+2) / (x+3)(x+1)
(6-x)/((x+3)(x-1)) * ((x+3)(x+1))/((x-6)(x+2))
(6-x)(x+3)(x+1)
-------------------------
(x-6)(x+2)(x+3)(x-1)
-(x+1)/((x+2)(x-1))
-(x+1)/(x^2+x-2)
From the final result we must exclude 1 and -2
However, (C) is not the answer, since in the original expression, -3 and 6 must also be excluded, since they produced zero in fraction denominators.
So, (A) is the answer.
The terms are powers of 3, so it's a geometric sequence with common ratio 3. So,
S10 = 1(3^10-1)/(3-1) = 29524
Can you help on one more question?
bring it on!
What is S10 for 1+2+9+27+...? The 10 is small and below the S.
A: 9,841
B: 29,525
C: 14,762
D: 29,524