Algebraic Fractions

Understanding Algebraic Fractions

An algebraic fraction is simply a fraction where the numerator and/or the denominator are algebraic expressions, for example: x/y, or (2x+1)/(x-2).
Like numerical fractions, algebraic fractions can be added, subtracted, multiplied, and divided.
The operation principles of numerical fractions fully apply to algebraic fractions.

Simplifying Algebraic Fractions

Simplification of algebraic fractions is crucial in solving algebraic equations.
The process involves factorising the numerator and the denominator to identify common factors that can be cancelled out.
For instance, the fraction (2x+4)/2x simplifies to (2(x+2))/2x and further simplifies to (x+2)/x after cancelling out common factors.

Adding and Subtracting Algebraic Fractions

When adding or subtracting algebraic fractions, make sure the denominators are the same, just like with numerical fractions.
If the denominators are not the same, you need to find a common denominator by multiplying the denominators together.
For instance, to add x/4 and 2x/6, the common denominator is 12 (4 * 3 = 12, 6 * 2 = 12). So, x/4 becomes 3x/12 and 2x/6 becomes 4x/12.
After ensuring the denominators are the same, you can now add or subtract the numerators: 3x/12 + 4x/12 = 7x/12.

Multiplying and Dividing Algebraic Fractions

When multiplying algebraic fractions, you multiply the numerators together for the new numerator, and do the same with the denominators for the new denominator.
For example, x/3 multiplied by 2/4 gives (x * 2)/(3 * 4) = 2x/12, which further simplifies to x/6.
Dividing algebraic fractions involves flipping the second fraction (reciprocal) and then following the multiplication rules.
For instance, (x/3) divided by (2/4) becomes x/3 * 4/2 = (x * 4)/(3 * 2) which simplifies to 4x/6 or further to 2x/3.

By mastering these concepts, you’ll be able to work with algebraic fractions with confidence and ease, significantly enhancing your proficiency in Algebra.