Question

lets try this again
k here is the equation in words x minus 3 over x minus 1 minus 2x minus 4 over x minus 1 equals 0
sovle equation with rational expressions

Answer 1

This?
\[\frac{x-3}{x-1} - \frac{2x-4}{x-1} = 0\]


Add \(\large \frac{2x-4}{x-1} \) to both sides to start with, Then multiply both sides by (x-1) but be sure to recall that 1 cannot be a solution.

Answer 2

Then just solve for x.

Answer 3

yes that is it
i come up with 0 but not sure if that is a solution

Answer 4

\[\frac{x-3}{x-1} = \frac{2x-4}{x-1}\]\[\implies x-3 = 2x - 4, \ \forall x \ne 1\]\[\implies x = 1, \forall x \ne 1\] \[\implies \text{No solutions}\]

Answer 5

I'm not sure how you come up with 0. The only possible solution is 1, but it cannot be 1 because you'd have a 0 in the denominator.

Answer 6

k tell me if here is what i got see if it is right

(x-3)/(x-1)-(2x-4)/(x-1)=0
(x-3)/(x-1)-(2x-4)/(x-1)+(2x-4)/(x-1)=0+(2x-4)/(x-1)
(x-3)/(x-1)=(2x-4)/(x-1)
(x-3)/(x-1) (x-1)=(2x-4)/(x-1) (x-1)
x-3=2x-4
2x-x=3-4
x=-1

Answer 7

i have an idea

Answer 8

this is what i keep coming up with sorry not one

Answer 9

why don't we just subtract. after all, the denominators are the same

Answer 10

oops not 0 but i was not sure if that was a solution or not

Answer 11

yeah you can but my instructor want step by step like he does it

Answer 12

which i am not even sure i got the correct answer

Answer 13

\[\frac{x-3}{x-1} - \frac{2x-4}{x-1} = 0\]
\[\frac{x-3-(2x-4)}{x-1}\]
\[\frac{-x+1}{x-1}=0\]
\[-1=0\] a contradiction

Answer 14

the left hand side of the equation is a number. it is minus one. the right hand side is zero. there is no solution

Answer 15

k here is my solutiuon see if it is right i also have one more for someone to look at to see if i got it right

Answer 16

@cherryblossoms you wrote the answer is
\[x=-1\] but x cannot be minus one. is it clear why?

Answer 17

ok so i need to move the x to the other side and the -1 to the op side correct

Answer 18

she made a mistake above
she has
(x-3)/(x-1)-(2x-4)/(x-1)=0
(x-3)/(x-1)-(2x-4)/(x-1)+(2x-4)/(x-1)=0+(2x-4)/(x-1)
(x-3)/(x-1)=(2x-4)/(x-1)
(x-3)/(x-1) (x-1)=(2x-4)/(x-1) (x-1)
x-3=2x-4
2x-x=3-4 <- but here a mistake happens x-2x=3-4
x=-1 -x=-1
x=1

but x cannot be 1 since we cannot have 0 on bottom

Answer 19

ok that attachment you have is right
but you need to go back and say x=1 is not a solution