Simplifying Rational Expressions

Simplifying Rational Expressions

How to simplify rational expressions: examples and their solutions.

Example 1

Simplify the given expression. (x - 5)/(x^2 - 7x + 10)

Factor the denominator:
x2 - 7x + 10 = (x - 5)(x - 2)

Cancel the common factor (x - 5).

Example 2

Simplify the given expression. (2a^2 + a - 1)/(a^2 - 2a - 3)

Factor the numerator and the denominator:

2a2 + a - 1 = (2a - 1)(a + 1)
a2 - 2a - 3 = (a + 1)(a - 3)

Cancel the common factor (a + 1).