They use rational equations for fun in the evening to relax.
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a rational function.
Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.
They are the solutions for the reduced quadratic.
Simultaneous equations can also be solved by substitution or graphically
You plug the number back into the original equation. If you have a specific example, that would help.