Respuesta :
Solution:
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials. This type of equation can lead to extraneous solution.
Example;
[tex]\begin{gathered} \frac{x^2+3x}{x+2}=\frac{-2x-6}{x+2} \\ \\ \text{ Multiply both sides by }(x+2)\text{ gives;} \\ x^2+3x=-2x-6 \\ x^2+5x+6=0 \\ x=-2,x=-3 \end{gathered}[/tex]Here, if we check the solutions by substituting back into the original rational equation, then;
[tex]x=-2\text{ is not a solution because the given equation has zeros in the denominator}[/tex]Also, radical equation is an equation in which a variable is under a radical. This type of equation can lead to extraneous solution.
Example;
[tex]\begin{gathered} \sqrt{2-x}=x \\ \\ \text{ Square both sides gives;} \\ 2-x=x^2 \\ \\ x^2+x-2=0 \\ \\ x^2+2x-x-2=0 \\ \\ x+2=0,x-1=0 \\ \\ x=-2,x=1 \end{gathered}[/tex]Here, if we check the solutions by substituting back into the original radical equation, then;
[tex]x=-2\text{ is not a solution because the solution after substitution is }2\text{ not }-2[/tex]FINAL ANSWER: Rational Equations and Radical Equations
