Question

x+1/x=2 find the value of x/x+1+x*x

Answer 1

$\boxed{\huge\mathfrak\color{red}answer}$

Question:$\frac{x + 1}{x} = 2$

$\implies \: x + 1 = 2x$

$\implies \: x = 2x - 1$

Now putting the values of x in the second equation

$\frac{x}{ {x}^{2} + x+ 1}$

$\rightarrow \: \frac{2x - 1}{({2x - 1})^{2} + 2x - 1 + 1 }$

$\rightarrow \: \frac{2x - 1}{ {4x}^{2} - 4x + 1 + 2x }$

Now solving the quadratic equation in the denominator ,

$\rightarrow \frac{2x + 1}{ {4x}^{2} - 2x + 1 }$

$\rightarrow \frac{2x - 1}{ {4x}^{2} - 4x + 2x +1}$

$\rightarrow\frac{2x - 1}{(2x - 1)(2x + 1)}$

Now cancelling (2x-1) from both numerator and denominator we get,

$\boxed{ \frac{1}{2x + 1} }(answer)$