Question

Find the quotient of 48a^4-16a^2-32/8a^2-8

Answer 1

We know that if we had
8/6=2/2 times 4/3=1 times 4/3=4/3
find common factors in top and obttom
factor
48a^4-16a^2-32=(16)(a-1)(a+1)(3a^2+2)
8a^2-8=8(a-1)(a+1)
so we have
$\frac{48a^4-16a^2-32}{8a^2-8} = \frac{(2)(8)(a-1)(a+1)(3a^2+2)}{(8)(a-1)(a+1)}= (\frac{8}{8}) (\frac{a-1}{a-1})( \frac{a+1}{a+1}) ( \frac{(2)(3a^{2}+2)}{1})=$(2)(3a^2+2)=6a^2+4


answer is 6a^2+4