Question

Rational Equation with Extraneous Solutions

A) Solving Rational Equations
B) Eliminating Extraneous Roots
C) Rationalizing Solutions
D) The Rational Equation Paradox

Answer 1

A rational equation with extraneous solutions refers to an equation that may produce solutions that do not satisfy the original equation. To solve these equations, you need to clear the equation of any denominators, simplify, and check for extraneous solutions.

Step-by-step explanation:

The subject of this question is Mathematics.

A rational equation with extraneous solutions refers to an equation that, when solved, may produce solutions that do not satisfy the original equation. To solve rational equations, you can follow these steps:

1. Identify any restrictions on the variable (values that make the denominator equal to zero).
2. Clear the equation of any denominators by multiplying both sides by the LCD (Least Common Denominator) of all the fractions.
3. Simplify the equation and solve for the variable.
4. Check your solutions by substituting them back into the original equation to ensure they are valid and not extraneous.

If any of the solutions from step 3 are not valid in the original equation, they are considered extraneous solutions and must be eliminated.