SOLUTION: How to solve the following problems (with exact solutions): (2)/(x-1)+x= 5 and (2)/(x-1)+x= 2 (This has to do with rational functions)

Question 825190: How to solve the following problems (with exact solutions):
(2)/(x-1)+x= 5 and (2)/(x-1)+x= 2
(This has to do with rational functions)
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
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:

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.
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