What is rational expression?
A rational expression is simply a fraction that contains algebraic expressions. For example, \(\frac{x^2 - 7x + 12}{x^2 + x - 20}\)
Just like numbers can be simplified, algebraic fractions can also be simplified.
Simplification of rational expression:
(1) Factorise the numerator.
(2) Factorise the denominator.
(3) Cancel the common factors.
(4) Write the simplified form of the expression.
Example:
Simplify the expression \(\frac{x^2 - 7x + 12}{x^2 + x - 20}\)
Solution:
Let us factorise the numerator and denominator separately.
\(x^2 - 7x + 12 = x^2 - 3x - 4x + 12\)
\(= x(x - 3) - 4(x - 3)\)
\(= (x - 4) (x - 3)\)
\(x^2 + x - 20 = x^2 + 5x - 4x + 20\)
\(= x(x + 5) - 4(x + 5)\)
\(= (x - 4) (x + 5)\)
Now, cancel the common factors.
\(\frac{x^2 - 7x + 12}{x^2 + x - 20}\) \(=\) \(\frac{(x - 4) (x - 3)}{(x - 4) (x + 5)}\)
\(=\) \(\frac{(x - 3)}{(x + 5)}\)
Thus, \(\frac{x^2 - 7x + 12}{x^2 + x - 20}\) \(=\) \(\frac{x - 3}{x + 5}\).