Algebraic Fractions
Algebraic fractions are simply fractions with
algebraic expressions on the top and/or bottom.
When adding or subtracting algebraic fractions, the first
thing to do is to put them onto a common denominator (by cross
multiplying).
e.g. 1 + 4 (x
+ 1) (x + 6)
= 1(x + 6) +
4(x + 1) (x + 1)(x + 6)
= x + 6 + 4x + 4 (x +
1)(x + 6)
= 5x + 10 (x + 1)(x + 6)
Solving equations
When solving equations containing algebraic fractions, first multiply both
sides by a number/expression which removes the fractions.
Example
Solve 10 
2 = 1 (x +
3) x
multiply both sides by x(x + 3): \ 10x(x + 3)  2x(x + 3) = x(x
+ 3) (x + 3) x
\ 10x  2(x + 3) = x² + 3x [after
cancelling] \ 10x  2x  6 = x² + 3x \ x²  5x + 6 = 0 \ (x  3)(x  2) = 0 \ either x = 3 or x = 2
Copyright © Matthew Pinkney 2003
