Question

If $f$ is an even function defined on the interval $(-5,5)$ then find the total number of real values of $x$ satisfying equation $f\left(x\right)=\left(\frac{x+1}{x+2}\right)$ are

Answer 1

If $f\left(x\right)$ is an even function in $(-5,5)$

$f\left(x\right)f(-x)$

$\frac{x+1}{x+2}=\frac{-x+1}{-x+2}$

$(x+1)(2-x)=(x+2)(1-x)$

$2x-x^2+2-x=x-x^2+2-2x$

$x+2=-x+2$

$2x=0$

$x=0$

one real value in $(-5,5)$