Help #3 ​

First one:  First let's factor the numerator and denominator

Numerator   z^2  (z+1)(z+2)

Denomin    (z+1) (z)(z+3)

Second determine what values of z are not allowed (those that would make either denominator = 0 are not allowed)

z = 0 or -1  or -3   are not allowed

Now cancel out the term (z+1) and you are left with

z^2(z+2) / z(z+3)   Simplify   (one more z will cancel out)

(z)(z+2) / (z+3)   =  (z^2 +2z) / (z+3)

Your second question is similar to the first (but remember ...when you divide by a fraction you flip it over and multiply)   Remember to find the values of x which are not allowed in the denominators before you flip it

4.

x + 2               x + 4   

____     ÷       _________           factor the denominator on the right

x  - 1              x^2 +4x - 5

x + 2              x + 4

____   ÷         __________         notice that x  cannot be  1  or  -5

x - 1              (x - 1) ( x + 5)  

So....we actually have

x + 2             (x - 1) (x + 5)

_____    x   ____________     =

x  -  1              x + 4

( x + 2) ( x - 1) ( x - 5)

__________________          the  (x -1)'s   cancel and we're left with

  (x - 1) ( x + 4)

( x + 2)( x - 5)

___________       Notice that we have another restriction......x cannot  = -4

      x +  4

So....the final answer is in red...and the restrictions are that x  cannot equal  1,-5, -4

So.....last answer