Hi ... i appreciate you to answer this questuion... \frac{ {x}^(2) }{ {x}^(4) + 1 } ​

Question

Hi ... i appreciate you to answer this questuion...


`\frac{ {x}^(2) }{ {x}^(4) + 1 }`
​

Answer 1

`\large \boxed{\sf \ \ (x^2)/(x^4+1)=(1)/(7) \ \ }`

Explanation:

Hello,

We know that (let's assume that x is different from 0 as we cannot divide by 0)

`x+(1)/(x)=3`

and we want to estimate

`(x^2)/(x^4+1)`

Let's take the square.

`9=3^2=(x+(1)/(x))^2=x^2+2\cdot x \cdot (1)/(x)+(1)/(x^2)=x^2+2+(1)/(x^2)=(x^4+1)/(x^2)+2`

So, we can write

`(x^4+1)/(x^2)=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\(x^2)/(x^4+1)=(1)/(7)`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you