How do I simplify [(x^2 + 4x- 12) / (x^2 - 25) ] / [(x+6) / (x^2-5x)] ?

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1) Remember your basic fraction rules (A/B) / (C/D) = (A/B) x (D/C)

(Apply this to the problem above but leave as seperate fractions to enable you to cancel it down easily later). 

[(x2 + 4x- 12) / (x2 - 25) ] * [(x2-5x) / (x+6)]

2) Factorise each of the numerators and denominators individually

[((x-2) (x+6)) / ((x+5) (x-5))] * [(x(x-5)) / (x+6)]

3) Cancel alike terms that are common on the numerator and denominator

[((x-2) (x+6)) / ((x+5) (x-5))] * [(x(x-5)) / (x+6)]

 = [x(x-2) / (x+5)]

Emma W. A Level Extended Project Qualification tutor, A Level Geograp...

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