Simplifying Aqa Higher

Simplifying algebraic fractions

What is an algebraic fraction?

• An algebraic fraction is a fraction with an algebraic expression on the top (numerator) and/or the bottom (denominator)

How do you simplify an algebraic fraction?

• If possible, factorise fully the top and bottom

  • E.g.

• Cancel common factors

  • This factor may be a single term

    • E.g.

  • It could also be a common bracket

    • E.g. <img alt=”fraction numerator x up diagonal strike open parentheses x plus 2 close parentheses end strike over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x minus 1 close parentheses end fraction equals fraction numerator x over denominator x minus 1 end fraction” data-mathml=”<math ><semantics><mrow><mfrac><mrow><mi>x</mi><menclose notation=”updiagonalstrike”><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></menclose></mrow><mrow><menclose notation=”updiagonalstrike”><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></menclose><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mi>x</mi><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%22166%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmenclose%20notation%3D%22updiagonalstrike%22%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmenclose%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmenclose%20notation%3D%22updiagonalstrike%22%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmenclose%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fm