Question

More complex fractions. How should I solve this one?

Answer 1

\[\frac{ \frac{ 1 }{ z-7 } +\frac{ 7 }{ z }}{ \frac{ 1 }{ z^2-7z } -1}\]

Answer 2

it was a pain to write that...

Answer 3

multiply through by z(z-7)

Answer 4

the common denominator of the 4 fractions

Answer 5

so multiply by z just by the top part of the fraction?

Answer 6

\[[\frac{ 1 }{ z-7 } + \frac{ 7 }{ z }] * [z(z-7)]\]

Answer 7

that is the numerator

Answer 8

so \[\frac{ 1 }{ z^2-7z }+\frac{ 7 }{ z^2}\]

Answer 9

for the numerator

Answer 10

it would come to

z + 7(z-7)

Answer 11

for what z^2-7z?

Answer 12

that is what the numerator simplifies to, you are going to multiply numerator and denominator by z(z-7)

Answer 13

\[[\frac{ 1 }{ z(z-7) } - 1]* [z(z-7)]\]

Answer 14

denominator goes to that...

1 - z(z-7)

Answer 15

@kmorgan

Answer 16

so overall this is what you have

\[\frac{ z + 7(z-7) }{ 1 - z(z-7) }\]

Answer 17

let me read that over..

Answer 18

i can type it all in one line here...

Answer 19

ahh the denominator of the numerator's first term would be z + 7(z-7)

Answer 20

\[\frac{ \frac{ 1 }{ z-7 }+ \frac{ 7 }{ z } }{ \frac{ 1 }{ z(z-7) } - 1 }*\frac{ z(z-7) }{ z(z-7) }\]

Answer 21

pretty sure there is z on top of the denominator's first numerator not a 1

Answer 22

\[\frac{ z + 7(z-7) }{ 1 - z(z-7) }\]

Answer 23

then the bottom would be z - z(z-7) instead

Answer 24

on the numerator isn't the denominator z(z-7) not x-7

Answer 25

i dont see an x. then you can now just multiply everything out if you want

Answer 26

so if i didn't change a thing on this question and just multiplied it out, i would still get the same answer?

Answer 27

i don't understand, what are you changing?

Answer 28

\[\frac{ 8z - 49 }{-z^2 + 7z + 1 }\]

Answer 29

this is all i have on my paper right now

\[\frac{ \frac{ 1 }{ z(z-7) }+\frac{ 7 }{ z^2 } }{ \frac{ z }{ z(z-7) } -1}\]

Answer 30

i got lost from there

Answer 31

the common denominator of the 4 sub fractions is, \[z^2*[z(z-7)]\]

Answer 32

you can multiply that whole thing by
\[\frac{ z^2[z(z-7)] }{ z^2[z(z-7)] }\]

Answer 33

So using distributive rule, multiply each fraction by z^2(z(z-7))

Answer 34

\[\frac{ z^2 + 7*z(z-7) }{ z*z^2 - z^2[z(z-7)] }\]

Answer 35

that gets rid of the fractions, now multiply all that out if you want