Question

Someone please help, reducing algebraic fractions to lowest terms.

Answer 1

1) \[\frac{ x+1 }{ x ^{2}-2x+1 }\]

Answer 2

you can factorise the denominator

Answer 3

So do I take x+1 out of the denominator? o_0

Answer 4

{the denominator is the bottom half of the fraction}

Answer 5

can you work out the factors?

Answer 6

if you need a clue its a prefect square

Answer 7

@nee5277

Are you clueless ?

Answer 8

@hba Obviously that is why I'm here... @UnkleRhaukus so I take it out of the \[x^{2}\]?

Answer 9

to factorise the denominator you could look at the factors of the single number term- and uses the fact that we have a perfect square ,
or you could used the quadratic forumla

Answer 10

Like 2x+1?

Answer 11

pardon ?

Answer 12

lol.

Answer 13

\[x^2-2x+1=(x+?)(x+?)=(x+?)^2\]

Answer 14

(x+1) (x+1)

Answer 15

not quite right , because \[(x+1)(x+1)=x^2+x+x+1=x^2+2x+1\]

Answer 16

I understand that part.. I don't understand the first step of how to reduce the fraction :/

Answer 17

we are not up to that bit yet,
you have to get the factorisation right first

Answer 18

Okay, so I get what you said up there.

Answer 19

can you find the factors to get \[x^2\color{red}−2x+1\]

Answer 20

Do you know how would you factorize the denominator ?

Answer 21

Not really.

Answer 22

to factorize any quadratic equation, we split the middle term, like here, we split the middle term -2x in 2 terms ax+bx
a,b are such that ab = 1 and a+b =-2
so can u find 2 such numbers a,b such that
ab = 1 and a+b =-2

Answer 23

a and b is equal to one.

Answer 24

not really, both a and b comes out to be negative in this case.

Answer 25

Ugh, I'm confused :/

Answer 26

if a=b=1, then a+b is not -2

Answer 27

I'm confused it says up there that a+b=-2 :l

Answer 28

yes, its easy, which 2 numbers have product =+1 but if u sum then u get -2 ?

Answer 29

\[x ^{2}-2x+1=(x-1)^2\]

Answer 30

\[\frac{ x+1 }{ (x-1)^2 }\]

Answer 31

we wanted to figure that out by yourself...

Answer 32

So wouldn't I cancle out x+1 from the top and bottom?

Answer 33

there is no x+1 in the bottom...

Answer 34

now

\[\frac{ x+1 }{ (x-1)^2 }=\frac{ x-1+1 }{ (x-1)^2 }=\frac{ x-1 }{ (x-1)^2 }+\frac{ 1 }{ (x-1)^2 }\]

Answer 35

\[(a-b)^2=a^2-2ab+b^2\]

Answer 36

I'm getting more confused.

Answer 37

Unkle, that just got complicated, and not 'reduced'

Answer 38

but now we can cancel

Answer 39

i thiink, (x+1)/(x-1)^2 is final answer, most reduced form....

Answer 40

well i was working towards

1 / (x-1) + 1/(x-1)^2