Algebraic Fractions: The Complete Guide
Multiplication is the easiest operation with algebraic fractions. Simply multiply the top terms together and the bottom terms together, then look for common factors to cancel out. For example, if you have y×y+1 on top and y+1×y+2 on bottom, you can cancel the y+1 from both parts.
Division follows the "Keep, Flip, Change" rule (KFC). Keep the first fraction as it is, change the division sign to multiplication, and flip the second fraction upside down. Then treat it as a multiplication problem.
Top Tip: Always look for terms you can cancel before doing any calculations - it'll save you loads of time!
Addition and subtraction require more steps but follow a clear pattern. First, multiply the denominators to create a common bottom. Then cross-multiply each numerator with the opposite denominator. Finally, add or subtract the new top numbers whilst keeping the common denominator, and simplify your answer.
Remember, you don't need to expand brackets unless specifically asked - keeping them factorised often makes cancelling much easier!