Question

What is the quotient in simplest form? State any restrictions on the variable.

(z^2 - 4)/(z - 3) divided by (z+2)/(z^2+z -12)

Answer 1

start by using the fact.... dividing by a fraction means you flip and multiply

so you get

\[\frac{z^2 -4}{x -3} \times \frac{z^2 + z -12}{z + 2}\]

next you should factor the quadratic expressions.

then cancel common factors...

hope it helps

Answer 2

Ok thanks :) Though can you explain how I find the restrictions?

Answer 3

yep the restrictions will occur with the denominator of the final answer..

you need to set the denominator to zero... and then solve for z.

the values will be the restrictions... as you can't have a zero denominator

Answer 4

\[\frac{z^2 -4}{x -3} \times \frac{z^2 + z -12}{z + 2}\]
\[=\dfrac{(x+2)(z-2)}{z-3} \times \dfrac{(z+4)(z-3)}{z+2}\]
\[=\dfrac{(z-2)}{1} \times \dfrac{(z+4)}{1}\]
\[=z^2 +2z-8\]
\[(z+4) (z-2)\]

So are the restructions when z = -4, 2?

Answer 5

well the denominator is a constant...1 ... so there are no restrictions in the final answer...

now go and look at the denominators of each faction in the question ans see if there are restrictions...

Answer 6

There is z = 3 and -2 correct?

Answer 7

I'd say z - 3 = 0 so z = 3



then z^2 + z - 12 = 0 (z +4)(z - 3) =0

so z = -4, 3

Answer 8

I see thanks :)
Also can there be more than just two restrictions?

Answer 9

well I would say if you are asked to graph it... there are 2 points of discontinuity

at x = 2 and x = 3...

but no major restrictions such as asymptotes...

I'm really unsure you you would be asked to find restrictions...

since the expression simplifies to a quadratic..

sorry I can't be more helpful