Question 825190
Rational EQUATIONS more so than functions.


First equation:  Multiply left and right sides by x-1, and simplify; solve for x.  Watch for a possible extraneous solution.  You would have a quadratic equation.


Second equation:  Similar to the first equation, multiply left and right sides by x-1, giving you a quadratic equation.  Solve for x; watch for a possible extraneous solution.


The multiplication of both sides by the denominator clears the rational expressions.


Follow this generalization:
{{{highlight_green(n/(x-a)+x=k)}}}
{{{n+x(x-a)=k(x-a)}}}
{{{n+x^2-ax=kx-ka}}}
{{{x^2-ax-kx=-n-ka}}}
{{{x^2-(a+k)x=-(n-ka)}}}
{{{highlight(x^2-(a+k)x+n-ka=0)}}}
OR
{{{highlight(x^2-(a+k)x+(n-ka)=0)}}}
Depending on the values you have for a, n, and k, you would either finish by factoring or finish by general solution to the quadratic formula.