Question

subtracting rational functions

Answer 1

@agent0smith i think i got it , i just need guidance

Answer 2

Okay.

Answer 3

\[\frac{ z^2 - 4z - 21 }{ z^2 - 5z - 24} - \frac{ z^2 - 15z + 56 }{ z^2 - 10z + 21 }\]

Answer 4

Factor everything first, will likely help now or later.

Answer 5

\[\frac{ ( z + 3 ) ( z - 7 ) }{ ( z - 8 ) ( z + 3 )} - \frac{ ( z - 8 )( z - 7 ) }{ ( z - 3 ) ( z - 7 )}\]

Answer 6

wouldnt i multiply the right side by ( z - 8 ) ( z + 3 ) and the left side by ( z - 3 ) ( z - 7 ) ?

Answer 7

Sure, if you want a mess of quartics :P Simplify before that... look for common factors.

Answer 8

lol omg how do i do that ?

Answer 9

Haha you know how to do it, you did in the last question! Look the fractions you just posted. Look for common factors to cancel.

Answer 10

\[\frac{ ( z+ 3 )(z-7)(z-3)(z-7) - (z-8)(z-7)(z-8)(z+3) }{ (z-8)(z+3)(z-3)(z-7) }\]

Answer 11

wouldnt everything cancel out ?

Answer 12

Woahhhh slow down. \[\Large \frac{ ( z + 3 ) ( z - 7 ) }{ ( z - 8 ) ( z + 3 )} - \frac{ ( z - 8 )( z - 7 ) }{ ( z - 3 ) ( z - 7 )}\]look closely...

Answer 13

( z - 7 ) cancels out , ( z - 8 ) cancels out and & ( z + 3 ) ?

Answer 14

z-8 doesn't. Remember you are looking at each fraction individually. The left, THEN the right.

Answer 15

ohhhhhhhhhhh i see i see ,

Answer 16

\[\frac{ ( z - 7 ) }{ ( z - 8 ) } - \frac{ ( z - 8 ) }{ ( z - 3 ) }\]

Answer 17

now i combine them ?

Answer 18

You need a common denominator first. What is missing from the denominator of the left? And the right?

Answer 19

from the left ( z - 3 ) & from the right ( z - 8 ) ?

Answer 20

Excellent.

Answer 21

\[\frac{ ( z - 7 ) ( z - 3 ) - ( z - 8 ) (z-8) }{ (z-8) ( z-3) }\] ?

Answer 22

Exactly.

Answer 23

ok let me try to do the rest , hold up

Answer 24

\[\frac{ -26z + 85 }{ ( z - 8 ) ( z - 3 ) }\]

Answer 25

looks like you forgot a negative\[\Large \frac{ ( z^2-10z+21) - (z^2 -16z+64) }{ (z-8) ( z-3) }\]

Answer 26

im right ? i mean my answer matches my answer choices

Answer 27

Check your work... you didn't distribute that negative.

Answer 28

Both your numerator numbers are wrong.

Answer 29

i foiled out my ( z-7 ) ( z - 3 ) - ( Z -8 ) ( Z - 8 ) In my numerator

Answer 30

wait wait wait hold up

Answer 31

Looks like you did that correct, just not this final step \[\Large \frac{ ( z^2-10z+21) - (z^2 -16z+64) }{ (z-8) ( z-3) }\]

Answer 32

oh i didnt distribute the negative

Answer 33

\[\frac{ 6z - 43 }{ ( z - 8 ) ( z - 3 ) }\]

Answer 34

Very good.

Answer 35

okay i have this answer choice as well haha , thank youuu (:

Answer 36

Welcome <3