Answer
There are no points of this function where the tangent line is parallel to $y=x$
Work Step by Step
The derivative of a function is the slope of the tangent line of that curve. So if we want points where the tangent line is parallel to y=x, both slopes must be the same, which is 1.
Then we have to derivate the function using the quotient rule, and after that equal this derivative to 1 and solve the quadratic equation, which is done on the image below.
But doing so we find $\frac{-2}{(x+1)^{2}}=1$, a false equality with no solution for x, since (x+1)^{2} is positive, and the division of a negative number by a positive number cannot be 1 (a positive number). This means there are no points of this function where the tangent line has such a slope.
