Algebraic Fractions (Equations) - GCSE Higher Maths

The video introduces solving equations with algebraic fractions, building on a previous video about algebraic fraction operations. The first step typically involves combining fractions on one side by finding a common denominator.

The first example demonstrates combining two fractions with numerical denominators (6 and 4). The lowest common multiple (LCM) is 12. The numerators are adjusted, expanded, and like terms are collected. The equation is then solved for x, yielding x = 5.4.

This example increases difficulty with numerical denominators 6 and 9, using an LCM of 18. Emphasis is placed on careful handling of negative signs when expanding brackets. The solution is found to be x = 4.

The third example introduces algebraic denominators (x+2 and x+5). The common denominator is their product. After combining fractions, expanding, and simplifying, the equation transforms into a quadratic equation, which is then factorized to find solutions x = -4 and x = 1.

This advanced example involves algebraic denominators leading to a quadratic equation that doesn't factorize simply. The video demonstrates using the quadratic formula, simplifying surds, and matching the answer to a specified format (a ± √13 / b). The solution involves x = (2 ± √13) / 3.

The final example presents a very complex equation with algebraic denominators and a fractional constant on the right side. The process involves finding a common denominator, expanding, clearing fractions by multiplying, and simplifying terms to obtain a quadratic equation. This quadratic is then factorized to find solutions x = 8.5 and x = 1/3.