# A simple C2 Q (abt fractions)

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#1
Express 3 / x^2+2x + x-4 / x^2-4 as a single fraction in its simplest form. (7 marks?!)
0
16 years ago
#2
(Original post by *girlie*)
Express 3 / x^2+2x + x-4 / x^2-4 as a single fraction in its simplest form. (7 marks?!)
Factorise then give the two parts the same denominator:
3/x(x+2) + (x-4)/(x+2)(x-2)
=3(x-2)/x(x+2)(x-2) + (x-4)(x)/x(x+2)(x-2)
=3(x-2)+(x-4)(x) / x(x+2)(x-2) then multiply the top and tidy up.
0
16 years ago
#3
3/[x^2+2x] + (x-4)/[x^2-4]
3/[x(x+2)] + (x-4)/[(x+2)(x-2)]
[3(x-2)/[x(x+2)(x-2)] + x(x-4)/[x(x+2)(x-2)]
[3(x-2) + x(x-4)]/[x(x+2)(x-2)]
[3x - 6 + (x^2) - 4x]/[x(x+2)(x-2)]
[(x^2) - x - 6)]/[x(x+2)(x-2)]
[(x-3)(x+2)]/[x(x+2)(x-2)]
[(x-3)]/[x(x-2)]
[(x-3)]/[(x^2) - 2x]
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#4
Thank you!
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