+37157 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
+130071 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
