Algebraic Fractions

Understanding Algebraic Fractions

• Algebraic fractions are fractions where the numerator and/or the denominator are algebraic expressions.
• Like ordinary fractions, they follow the same rules for addition, subtraction, multiplication, and division.

Simplifying Algebraic Fractions

• An algebraic fraction is in its simplest form when the greatest common divisor (GCD) of its numerator and denominator is 1.
• To simplify an algebraic fraction, factorise the numerator and the denominator and then cancel out common factors.
• Be careful with minus signs and double-check your work.

Adding and Subtracting Algebraic Fractions

• Like normal fractions, to add or subtract algebraic fractions, they must have a common denominator.
• A common denominator is the least common multiple (LCM) of the two denominators.
• Once the denominators are the same, add or subtract the numerators and simplify if possible.

Multiplying Algebraic Fractions

• When multiplying algebraic fractions, multiply the numerators together to create a new numerator, and then do the same for the denominators.
• Simplify the fraction if possible.

Dividing Algebraic Fractions

• To divide algebraic fractions, multiply the first fraction by the reciprocal of the second fraction.
• Remember, the reciprocal of a fraction is obtained by switching the numerator and the denominator.
• Simplify the resulting fraction, if necessary.

Solving Equations Involving Algebraic Fractions

• To solve an equation involving algebraic fractions, first try to clear the fractions.
• Clearing the fractions usually involves multiplying through by a common denominator.
• This will often turn the equation into a simple linear or quadratic equation that can be solved using standard techniques.

Remember: Always simplify your final answer, if possible. Most importantly, practise plenty of example problems to master these techniques.