**Algebraic
Fractions**

**Algebraic fraction** or rational algebraic expression is
a fraction whose numerator or denominator or both numerator and denominator are
algebraic expressions. For example:

**Algebraic fraction** should have non-zero denominator. If the denominator
is zero (0) it is known as undefined or meaningless.

**Basic
Properties of Algebraic Fractions**

The algebraic fraction whose denominator is not a zero has the
following properties:

- The value of fraction does not change if
the numerator and denominator are multiplied by the same number.

- The value of fraction does not change if
the numerator and denominator are multiplied by the same polynomial.

- We can reduce the algebraic fractions by
cancelling the common factors from numerator and denominator.

The basic properties of the fraction help us to change algebraic
fractions with different denominators into the fraction with same denominators.
Such property of fractions makes easy to simplify the algebraic fractions.

**Look
at the following workout examples:**

*Example 1: For what value of x, are the following expressions
undefined?*

*Solution: *

*An
algebraic fraction is undefined when its denominator is 0. The denominator is x
here.*

* **∴** **for x = 0, the given algebraic fraction
is undefined.*

*An
algebraic fraction is undefined when its denominator is 0. The denominator is x
- 3 here.*

* **∴** **for x - 3 = 0 or x = 3, it is undefined.*

*An
algebraic fraction is undefined when its denominator is 0. The denominator is
2x - 3 here.*

* **∴** **for 2x - 3 = 0 or 2x = 3 or x = 3/2, it
is undefined.*

*Example 2: Reduce the following algebraic fractions into their
lowest terms:*

*Solution: *

*You can comment your
questions or problems regarding algebraic
fractions here.*

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