Multiplication.
- Factorise everything.
- Cancel common factors across numerators and denominators.
- Multiply remaining numerators; multiply remaining denominators.
Example. 2xx2β1βΓx+14x2β.
- Factor: x2β1=(xβ1)(x+1).
- Substitute: 2x(xβ1)(x+1)βΓx+14x2β.
- Cancel: (x+1) across numerator and denominator. 4x2/2x=2x.
- Result: (xβ1)Γ2x=2x(xβ1)=2x2β2x.
Division β keep, change, flip.
baβΓ·dcβ=baβΓcdβ.
Then multiply as above.
Example. x2β4x2+3xβΓ·xβ2x+3β.
- Flip: x2β4x2+3xβΓx+3xβ2β.
- Factor: x2+3x=x(x+3). x2β4=(xβ2)(x+2).
- Substitute: (xβ2)(x+2)x(x+3)βΓx+3xβ2β.
- Cancel (x+3) and (xβ2): x+2xβ.
Edexcel tip. Don't expand the brackets unless asked. Cancel factors first to simplify.