Rational Functions
What are rational functions? Rational functions also known as algebraic fractions are functions that can be expressed as the quotient of two polynomials. Rational functions can be expressed in two major forms. The transformational form and the quotient form.

1. The Transformational Form: The transformational form of a rational function is given by:
\(\begin{array}{l}f\left( x \right) = \frac{a}{{x - h}} + k\\\begin{array}{*{20}{c}}{{\rm{where}}}&{h = {\rm{ }}\begin{array}{*{20}{c}}{{\rm{Horizontal}}}&{{\rm{Shift}}}\end{array}}\end{array}\\\begin{array}{*{20}{c}}{{\rm{and}}}&{k = {\rm{ }}\begin{array}{*{20}{c}}{{\rm{Vertical}}}&{{\rm{Shift}}}\end{array}}\end{array}\end{array}\)

2. The quotient Form: The quotient form as the name suggests is simply expressing the rational as the quotient of two polynomial function. This form is given by:
\(\begin{array}{l}f\left( x \right) = \frac{{N\left( x \right)}}{{D\left( x \right)}}\\{\rm{where}}\\\begin{array}{*{20}{c}}{N\left( x \right) = }&{{\rm{The}}}&{{\rm{Numerator}}}&{{\rm{Function}}}&{}\\{D\left( x \right) = }&{{\rm{The}}}&{{\rm{Denominator}}}&{{\rm{Function}}}&{}\end{array}\end{array}\)
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Examples of Rational functions are as follows
​\(\begin{array}{l}f\left( x \right) = 3{x^2} + 3x = \frac{{3{x^2} + 3x}}{1}\\f\left( x \right) = \frac{{2\left( {x - 2} \right)}}{{\left( {x + 2} \right)}}\\f\left( x \right) = \frac{4}{{{x^2} - 3x - 4}}\end{array}\)

HOW TO SOLVE RATIONAL EQUATIONS
1.Rewrite terms with their denominators equal to their LCD
2.Eliminate all denominators by multiplying by the LCD
3.Solve and Check​