Question

what is (x - 1)/(x^2 - 2x) - 2/(x^2 - 4) = 0

show all the steps to get there please... i know that the answer is (x + 1)/(x(x+2)) but i don't understand how to get there.

Answer 1

Can you show a screenshot plz?

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Trickjoker
It would be x=1±√5
\(\color{#0cbb34}{\text{End of Quote}}\)
i used mathway and another website to get the answer of (x+1)/(x(x+2)) and i know that it's correct but i need to show my work and i don't understand how to get there

Answer 3

Can you post a ss?

Answer 4

Oh.

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Can you post a ss?
\(\color{#0cbb34}{\text{End of Quote}}\)
my laptop doesn't let me ss it's weird

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @PinkGlitterz
\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Can you post a ss?
\(\color{#0cbb34}{\text{End of Quote}}\)
my laptop doesn't let me ss it's weird
\(\color{#0cbb34}{\text{End of Quote}}\)
Oh

Answer 7

This is kinda hard to solve bc i cant see the actual problem

Answer 8

here's the original problem

Answer 9

Oh ok thank you

Answer 10

\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Oh ok thank you
\(\color{#0cbb34}{\text{End of Quote}}\)
did you get anything yet?

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @PinkGlitterz
\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Oh ok thank you
\(\color{#0cbb34}{\text{End of Quote}}\)
did you get anything yet?
\(\color{#0cbb34}{\text{End of Quote}}\)
Hold on I’m checking if I’m right

Answer 12

\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
\(\color{#0cbb34}{\text{Originally Posted by}}\) @PinkGlitterz
\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Oh ok thank you
\(\color{#0cbb34}{\text{End of Quote}}\)
did you get anything yet?
\(\color{#0cbb34}{\text{End of Quote}}\)
Hold on I’m checking if I’m right
\(\color{#0cbb34}{\text{End of Quote}}\)
okay

Answer 13

Nope I was wrong lemme get one of the smart ppl to help @AZ @Jhonny9

Answer 14

Wait wrong person @johnyy9

Answer 15

Srry I’m slow @Jhonyy9

Answer 16

\(\color{#0cbb34}{\text{Originally Posted by}}\) @CripQUEZZ
Srry I’m slow @Jhonyy9
\(\color{#0cbb34}{\text{End of Quote}}\)
how did you try to solve it?

Answer 17

This is your question:
\(\dfrac{-2}{x^2 - 4} + \dfrac{x-1}{x^2-2x}\)

You need to know this rule:

\(\dfrac{a}{c} + \dfrac{b}{c} = \dfrac{a+b}{c}\)

So to add the fractions we need to have the same denominator.

The first step is to factor the denominator

you need to know one of this rule:
\( a^2 - b^2 = (a-b)(a+b)\)

so let's factor the denominators for both of the fractions, okay?

Answer 18

\(\dfrac{-2}{x^2 - 4} + \dfrac{x-1}{x^2-2x}\)


\(\dfrac{-2}{(x-2)(x+2)} + \dfrac{x-1}{x(x-2)}\)

so now we want them to have the same denominator for both

so for the first fraction, multiply x on both the numerator and denominator
for the second fraction, multiply (x+2) on both the numerator and denominator

Answer 19

Tell me what you get when you multiply the first fraction by x and the second one by (x+2)

remember, you have to do it to both the numerator and denominator
because when you do it to both, you're keeping the fraction equal. If you don't do it to the top and bottom then you're changing the fraction

Because multiplying by x/x is like multiplying by 1

So what do you get when do what I just told you to do?
After that we can add the fractions and try to simplify it more

Answer 20

Anyway, I worked through it up to this point since you're offline so that way whenever you come back online and if I'm not on, you wouldn't be stuck (:

Answer 21

@AZ okay so once I multiplied the numerator and denominator of the first fraction by x i got -2x/x^3-4x

Answer 22

and then once i mulitplied the second fraction i got x^2+x-2/x^3-4x

Answer 23

does that look right?

Answer 24

yes, although I would say to keep the denominator written as the factors because we can simplify it more

\( \dfrac{-2x}{x(x-2)(x+2)} + \dfrac{x^2 +x-2}{x(x-2)(x+2)}\)

and now add the numerators, what do you get?

and then you can factor the numerator and we'll be able to simplify it to your final answer

Answer 25

i got x^2 - x -2. is this correct?

Answer 26

yes, now can you factor it?

Answer 27

yeah! Factoring got me (x+1)(x-2)

Answer 28

and so then you (x-2) in the numerator and denominator and both cancel out and you get your final answer!

Answer 29

what do i do with (x-2) exactly? do i cancel it from both fractions' denominators?

Answer 30

uh

Answer 31

when you add the fractions, it only one denominator

you can only add/subtract fractions if the denominator is the same

\(\dfrac{a}{c} + \dfrac{b}{c} = \dfrac{a+b}{c}\)

Answer 32

right! sorry i was looking at my previous work haha. okay so with the denominators added together, i'm not sure what to do with the added numerator of -2x. was that supposed to be added into the numerator? because i dont have that in my factoring

Answer 33

I thought you did?

that's how you went from

-2x + x^2 + x - 2

to x^2 - x - 2
which you then factored into
(x+1)(x-2)

Answer 34

oh! my bad that's right- bear with my limited knowledge of algebra... i had no time to study for this lol and i'm sleep deprived

Answer 35

so then the final product is (x+1)(x-2) / x(x-2)(x+2) ?

Answer 36

@AZ

Answer 37

and you have (x-2) in the numerator and denominator so you can cancel it out

it's like when you have

\(\dfrac{2 \times 3}{2 \times 5} = \dfrac{3}{5}\)

Answer 38

\(\color{#0cbb34}{\text{Originally Posted by}}\) @PinkGlitterz
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Trickjoker
It would be x=1±√5
\(\color{#0cbb34}{\text{End of Quote}}\)
i used mathway and another website to get the answer of (x+1)/(x(x+2)) and i know that it's correct but i need to show my work and i don't understand how to get there
\(\color{#0cbb34}{\text{End of Quote}}\)

and that's how you get this final answer

Answer 39

okay thanks a bunch! i seriously can't thank you enough haha. i'm having such a hard time focusing operating on like 4 hours of sleep- so seriously thank you so much

Answer 40

Don't mention it!! It was my pleasure :)