Answer to Question #199710 in Algebra for Moe

Question

Note vector notation: (vector 1;vector 2)

Select the correct answer:

k(k-1) • • • (k-r)(m+1)m• • • 3• 2

_________________________ =

p(p-1)• • • (p-m)(r+1)r• • • 3• 2• 

a) (k;r) / (p+1 ; m)

b) (p;r) / (k+1 ; m)

c) (k;r) / (p ; m + 1)

d) (k;r) / (m+1 ; p)

e) (k; r +1) / (p ; m)

f) (k; r + 1) / (p ; m+1)

Answer 1

$\frac{k\left(k-1\right)\cdot \left(k-r\right)\left(m+1\right)m}{p\left(p-1\right)\cdot \left(p-m\right)\left(r+1\right)r}$

$=\frac{km\left(k-1\right)\left(-r+k\right)\left(m+1\right)}{r^2p^3+rp^3-r^2mp^2-rmp^2-r^2p^2-rp^2+r^2mp+rmp}$

$=\frac{k^3m^2+k^3m-k^2rm^2-k^2rm-k^2m^2-k^2m+krm^2+krm}{r^2p^3+rp^3-r^2mp^2-rmp^2-r^2p^2-rp^2+r^2mp+rmp}$

From the above expression, the answer is d) (k;r) / (m+1 ; p)