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Mathematics 7 Online
OpenStudy (anonymous):

If x-(1/x)=1 then (x^4-(1/x^2))/3x^2+5x-3 is

OpenStudy (anonymous):

3x^2+5x-3 can be written as divided it by x so 3x+5-3/x 3(x-1/x)+5 so it is 8

OpenStudy (anonymous):

then numerator (x^2-1/x)^2

OpenStudy (anonymous):

i feel numerator i am not getting

OpenStudy (anonymous):

(x^2-1/x)(x^2+1/x)so we get x^4-1/x^2

OpenStudy (gorv):

yeah it is

OpenStudy (anonymous):

how to get numerator to x-1/x format

OpenStudy (gorv):

(x^4-1)/x^2=

OpenStudy (gorv):

u know x^4-1=(x^2-1)*(x^2+1)

OpenStudy (gorv):

and it is divided by x^2 in Q

OpenStudy (anonymous):

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

OpenStudy (gorv):

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

OpenStudy (gorv):

x^2=x*x take one x below each factor

OpenStudy (anonymous):

latex not working

OpenStudy (gorv):

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

OpenStudy (gorv):

x-1/x

OpenStudy (anonymous):

1*1

OpenStudy (anonymous):

1/8

OpenStudy (gorv):

other part \[\frac{ x^2 +1}{ x}=\frac{ x^2 }{ x }+\frac{ 1 }{ x }\]

OpenStudy (gorv):

x+1/x

OpenStudy (anonymous):

yes i was thinking about that only

OpenStudy (gorv):

numerator \[(x-\frac{ 1 }{ x})*(x+\frac{ 1 }{ x })\]

OpenStudy (anonymous):

x=1+1/x so x+1/x=x

OpenStudy (gorv):

(x-1/x)^2=1

OpenStudy (anonymous):

so it is 1/8

OpenStudy (gorv):

wait

OpenStudy (anonymous):

something went wrong over here

OpenStudy (gorv):

x^2+1/x^2-2=1 x^2+1/x^2=1+2=3

OpenStudy (anonymous):

yes

OpenStudy (gorv):

but (x+1/x)^2=x^2+1/x^2+1

OpenStudy (gorv):

but we know x^2+1/x^2 =3 we calculated just above

OpenStudy (anonymous):

there also 2 insead of 1

OpenStudy (gorv):

(x+1/x)^2=3+2=5

OpenStudy (gorv):

that will be 2 ..typin mistake

OpenStudy (gorv):

x+1/x=sqrt5

OpenStudy (gorv):

1*sqrt5/8 is ans

OpenStudy (anonymous):

no

OpenStudy (gorv):

what??

OpenStudy (anonymous):

yes see (x^2-1/x)*(x^2+1/x)

OpenStudy (gorv):

that will be x^2 not x

OpenStudy (anonymous):

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

OpenStudy (anonymous):

how

OpenStudy (gorv):

\[\frac{ x^4-1 }{ x^2}=\frac{ x^4}{ x^2 }-\frac{ 1 }{ x^2 }\]

OpenStudy (gorv):

got me ??

OpenStudy (anonymous):

\[\frac{ x^4-1 }{ x^2}=\frac{ x^4}{ x^2 }-\frac{ 1 }{ x^2 }\].i can only see this

OpenStudy (anonymous):

ohh i cant able to see do u calculation without using latex

OpenStudy (gorv):

\[\frac{ x^4 }{ x^2 }= x^2\]

OpenStudy (gorv):

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

OpenStudy (anonymous):

if we divide it by x^2 then 1/x becomes1/x^3

OpenStudy (anonymous):

x^4-1/x^2 yes

OpenStudy (gorv):

how ????

OpenStudy (gorv):

(x^4-1)/x^2

OpenStudy (gorv):

here x^2 divide whole term

OpenStudy (anonymous):

see the question above

OpenStudy (gorv):

(x^4-1/X^2)????

OpenStudy (anonymous):

(x^4-(1/x^2))/3x^2+5x-3

OpenStudy (gorv):

ohhhhhhh

OpenStudy (gorv):

sorryyy i think x^2 DIVID E WHOLE

OpenStudy (anonymous):

ohh very sorry u understood like that ah

OpenStudy (gorv):

thn u did right

OpenStudy (gorv):

above

OpenStudy (anonymous):

then proceed to get x-1/x

OpenStudy (gorv):

x-1/x=1 1/x=x-1

OpenStudy (gorv):

put this in that equation

OpenStudy (anonymous):

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

OpenStudy (gorv):

x-1/x=1 x-1=1/x put x-1 in place of 1/x

OpenStudy (gorv):

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

OpenStudy (gorv):

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

OpenStudy (anonymous):

then we get x^4-x^2+1

OpenStudy (gorv):

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

OpenStudy (anonymous):

ohh yes

OpenStudy (anonymous):

x^4-x^2+2x-1 divide by x^2 we get x^2-1+2/x-1/x

OpenStudy (anonymous):

sorry x^2-1+2/x-1/x^2

OpenStudy (anonymous):

x-1=x

OpenStudy (anonymous):

wrong now also x-(1/x)

OpenStudy (anonymous):

x-(1/x)=1

OpenStudy (anonymous):

1/x=x+1 okay

OpenStudy (gorv):

x-1

OpenStudy (anonymous):

(x-1)/x=1 so x-1=x right

OpenStudy (anonymous):

1/x=x+1

OpenStudy (gorv):

x-(1/x)=1

OpenStudy (anonymous):

can we call ganeshie

OpenStudy (anonymous):

yes

OpenStudy (gorv):

sure u can if u want :)

OpenStudy (anonymous):

x^2-1/x^2-1-2/x

OpenStudy (gorv):

frm where u get this ??

OpenStudy (anonymous):

x^4-x^2-2x-1 divide by x^2

OpenStudy (anonymous):

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

OpenStudy (gorv):

yeah

OpenStudy (gorv):

we didnt get by nowwht we want

OpenStudy (anonymous):

(x^2-x-1)(x^2+x+1) x^4-x^2-2x-1 divide by x^2 x^2-1/x^2-1-2/x

OpenStudy (gorv):

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

OpenStudy (gorv):

x-1/x=1

OpenStudy (gorv):

x+1/x-1-2/x=x-1-1/x

OpenStudy (gorv):

x-1/x=1 1-1=0

OpenStudy (gorv):

rosy got it ??

OpenStudy (anonymous):

no we didnt get it i think

OpenStudy (anonymous):

@ganeshie8

ganeshie8 (ganeshie8):

its hard to go through above work as so much was done above, but it seems u had a very good start in killing the denominator

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