Question

Show work!!! :D Medal may be rewarded! :O

5. (5 over y - 5) = (y over y - 5) - 1

6. (1 over 3x - 2) + (5 over x) = 0

Answer 1

5. \[\frac{ 5 }{ y - 5 } = \frac{ y }{ y - 5 } - 1\]

6.\[\frac{ 1 }{ 3x - 2 } + \frac{ 5 }{ x } = 0\]

Answer 2

@Firejay5 Are you ready for my explaination?? :)

Answer 3

yea

Answer 4

Ok so first I want to know if you know how to subtract fractions and numbers?

Answer 5

1. I suck fraction so don't even try to ask me
2. I am partially good with numbers

Answer 6

Ok that's ok I can help :)
When we want to subtract fractions and numbers we need a common denominator. In this question lets work with the left side ok

Answer 7

I mean the right side Sorry :P

Answer 8

So lets begin :)
This is what the equation is
\[\frac{ y }{ y-5 }-\frac{ 1 }{ 1 }\]
Do you agree??

Answer 9

I guess

Answer 10

Why aren't you confident??

Answer 11

I thought it would be y - 5

Answer 12

What do you mean? All I did to the right side of the equation was put 1 over 1 because all numbers are over 1. Are you still confused?

Answer 13

see before you can add or subtract the denominator must be the same and all of the denominators are y - 5, so it should be 1 over y - 5

Answer 14

You're on the right track but not quite. In order to have the same denominator you have to multiply both the numerator and denominator by \[y-5\] so it would be
\[\frac{ y }{ y-5 }-\frac{ y-5 }{ y-5 }\]
Does that make sense?

Answer 15

see that's the point I was making

Answer 16

Ok so can we proceed?? :P

Answer 17

yes

Answer 18

Ok so now we have the same denominator we can evaluate the numerators together
\[\frac{ y-(y-5) }{ y-5 }\]
does this make sense?

Answer 19

yes

Answer 20

Ok so now we see that there is a negative sign in front of the (y-5) so that negative will affect everything in the bracket. So...
\[\frac{ y-y+5 }{ y-5 }\]
Do you agree??

Answer 21

yes

Answer 22

Ok Can you take it from here then?

Answer 23

so do we have so far?: \[\frac{ 5 }{ y - 5 } = \frac{ y - y + 5 }{ y - 5 }\]

Answer 24

Yes but we are solving the right side in order to prove both sides. So finish the right side

Answer 25

Do I cross multiply or what???

Answer 26

No on the right side y-y+5 has two common terms which can be simplified

Answer 27

what 2 common terms

Answer 28

Y and Y so they cancel out