Question

y=(x+5)/(3x-15)-5/(x-5)-2/3

Answer 1

then what?

Answer 2

find all values of x such that y=0

Answer 3

find the common denominator first.

Answer 4

would it be 3x^2-30+75

Answer 5

no

Answer 6

It is 3(x-5), then follow the usual method

Answer 7

how did you get that?

Answer 8

Look carefully the denominators of each term, what the common expression their?

Answer 9

but only the first 2 of them have x in them
i see no common expression

Answer 10

sorry I am not mean to that but to say common factor

Answer 11

i am very confused

Answer 12

can I wright the give expression as \[\frac{ x+5 - 15 - 2(x-5) }{ 3(x-5) }\]?

Answer 13

ok

Answer 14

Can I?

Answer 15

yes

Answer 16

Thus what is 3(x-5)

Answer 17

the common factor?

Answer 18

that is what I am trying to explain.
Now, what is the simplified form of the above expression?

Answer 19

-x/3(x-5)

Answer 20

right -x/3(x-5) = 0
Then use criss cross method

Answer 21

what is criss cross?

Answer 22

multiply -x with 1 and 3(x-5) with 0

Answer 23

why? i will get -x

Answer 24

because the value of 3(x-5) is does not make the expression -x/3(x-5) zero. Which means the value of -x/3(x-5) to be zero 3(x-5) does not have any roll

Answer 25

so then y cannt = 3(x-5)

Answer 26

no to be y = 0, x must be zero

Answer 27

ok thanks!

Answer 28

y=(x+5)/(3x-15)-5/(x-5)-2/3
solve for y=0
\[ \frac{x+5}{3x-15} -\frac{5}{x-5}-\frac{2}{3}= 0\]
The first thing you should look for (hope for!) is that the complicated 3x-15 can factor into something simpler. You notice 3 divides evenly into 3x and into 15, so factor out 3:
3(x-5)
\[ \frac{x+5}{3(x-5)} -\frac{5}{x-5}-\frac{2}{3}= 0\]
now you can find a common denominator, or you can "clear the denominator"
Let's clear the bottom: first multiply all terms on both sides of the = sign by 3(x-5). This will "cancel" the bottom in the first term.
\[\cancel{ 3(x-5)}\cdot \frac{x+5}{\cancel{3(x-5)}} -3\cancel{(x-5)}\cdot \frac{5}{\cancel{x-5}}-\cancel{3}(x-5)\cdot \frac{2}{\cancel{3}}= 0\]

Answer 29

that mess simplifies to
\[ x+5 -3 \cdot 5 -(x-5)\cdot 2= 0\]
-3*5 is 15, and -(x-5)*2 is (-x+5)*2, or -2x+10:
\[ x+5-15 -2x+10 =0 \]
finally, 5-15+10= 0, and x-2x is -x:
-x=0 or x=0

Answer 30

-3*5 is -15, and -(x-5)*2 is (-x+5)*2, or -2x+10:

Answer 31

so the solution set would be 0,-0 ?

Answer 32

normally people do not attach a - to 0. it is just 0.
if you are asking what x,y pair is a solution then (0,0) is the answer