Question

x+1/x=3 then (x^3+1/x)/(x^2-x+1)=?​

Answer 1

Answer:

I hope it helps you.

refer to this attachment.

Answer 2

Answer:

Given equation is linear equation in one variable and after solving it we can find the value of x as:-)

Given that

$\frac{x + 1}{x} = 3 \\ \implies x + 1 = 3x \\ \implies 2x - 1 = 0 \\ \implies \boxed{ \boxed{ x = \frac{1}{2} }}$

Now,

to find the value of given expression we will put the value of x in the expression as:-)

$\dfrac{\dfrac{ {x}^{3} + 1 }{x} }{ {x}^{2} - x + 1} \\ \\ \\ = \displaystyle \dfrac{\dfrac{ \dfrac{1}{8} + 1 }{ \dfrac{1}{2} } }{ \dfrac{1}{4} - \dfrac{1}{2} + 1 } \\ \\ \\ = \dfrac{ \dfrac{9}{4}}{ \dfrac{3}{4} } \\ = 3$