Revision: fractional equations

A fractional equation has the unknown in the denominator as well. Before solving it you must impose the existence conditions (the denominators must be non-zero) and, at the end, check that the solutions found are acceptable. To verify that a value is a solution means to check that, on substituting it, the equality becomes true.

Example

For which value of $a$ does the equation $\frac{2x}{x-a} + \frac{3}{x^2-4} + 2 = 0$ have $x=5$ among its solutions? Requiring $x=5$ to be a solution means demanding that, on substituting $x=5$, the equality turns out true (a check). It is therefore enough to substitute $x=5$ into the equation and solve the resulting equation in the unknown $a$.

Links

Topics: Quadratic equations
Concepts: Existence conditions · Fractional equation · Checking the result
Skills: Solving equations