Question

I need help expressing this quotient in simplest form! Please explain it because I don't understand! Here is the quotient:
http://imgur.com/i63S5i1

Answer 1

Firstly factorise all of polynomials, then we can begin to pull out similar terms: \[\frac{ x^2-4 }{ x^3+7x^2 } \div \frac{ x^3-x^2-6x }{ x^2+4x-21 } = \frac{ (x-2)(x+2) }{x^2(x+7)} \div \frac{x(x-3)(x-2)}{(x+7)(x-3)}\]You should know that when you divide a fraction, it is the same as multiplying by the reciprocal (upside down) so now we have:
\[\frac{ (x-2)(x+2) }{x^2(x+7)} * \frac{(x+7)(x-3)}{x(x-3)(x-2)}\]We can cancel the numerators and denominators now, so firstly remove the (x-2) from the top and the bottom:\[\frac{ (x+2) }{x^2(x+7)} * \frac{(x+7)(x-3)}{x(x-3)}\]Now cancel the (x+7) from the top and the bottom:
\[\frac{ (x+2) }{x^2} * \frac{(x-3)}{x(x-3)}\]Now cancel the (x-3):
\[\frac{ (x+2) }{x^2} * \frac{1}{x}\]

We're left with:\[\frac{ (x+2) }{x^3}\]Which is your answer :)

Answer 2

Ohh Okay i seeeee! Yeah I forgot to factor everything in the beginning which is what mainly messed me up, so i was stumped.. thanks a lot! :)

Answer 3

Factorising polynomials tends to make them a lot more useful to us so it's always worth trying if you're stuck. No problem!