Mathematics
PinkGlitterz:

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.

CripQUEZZ:

Can you show a screenshot plz?

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

CripQUEZZ:

Can you post a ss?

Trickjoker:

Oh.

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

CripQUEZZ:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @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

CripQUEZZ:

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

PinkGlitterz:

|dw:1614804885990:dw|

PinkGlitterz:

here's the original problem

CripQUEZZ:

Oh ok thank you

PinkGlitterz:

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

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

PinkGlitterz:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @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

CripQUEZZ:

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

CripQUEZZ:

Wait wrong person @johnyy9

CripQUEZZ:

Srry I’m slow @Jhonyy9

PinkGlitterz:

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

AZ:

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?

AZ:

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

AZ:

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

AZ:

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 (:

PinkGlitterz:

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

PinkGlitterz:

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

PinkGlitterz:

does that look right?

AZ:

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

PinkGlitterz:

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

AZ:

yes, now can you factor it?

PinkGlitterz:

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

AZ:

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

PinkGlitterz:

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

AZ:

uh

AZ:

when you add the fractions, it only one denominator you can only add/subtract fractions if the denominator is the same $$\dfrac{a}{c} + \dfrac{b}{c} = \dfrac{a+b}{c}$$

PinkGlitterz:

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

AZ:

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)

PinkGlitterz:

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

PinkGlitterz:

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

PinkGlitterz:

@AZ

AZ:

and you have (x-2) in the numerator and denominator so you can cancel it out it's like when you have $$\dfrac{2 \times 3}{2 \times 5} = \dfrac{3}{5}$$

AZ:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @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

PinkGlitterz:

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

AZ:

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