Simplify Fractions: 4x²-6x/(4x²-9)

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thomas49th
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Homework Statement



Simplify fully the following equation

Homework Equations



[tex]\frac{4x^{2}-6x}{4x^{2}-9}[/tex]


The Attempt at a Solution



the 4x² cancel each other out and 3 goes into 6 and 9
so the answer is
[tex]\frac{-2x}{-3}[/tex]

but that seems to easy for the penultinate question on a higher GCSE paper.
 
Last edited:
Sorry, I missed it out in the equatio above... I've edited it in now

Thanks
 
You can't cancel out the 4x^2 like that! That's an illegal move.
 
Last edited:
You can only cancel out factors! never terms!

Handwritten simplification: (4x^2 - 6x)/(4x^2 - 9) = 2x(2x - 3)/((2x - 3)(2x + 3)) = 2x/(2x + 3) = 1/(1 + 3/(2x)).
 
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  • Simplification chain: (4x^2 - 6x)/(4x^2 - 9) = 2x(2x - 3)/((2x - 3)(2x + 3)) = 2x/(2x + 3) = 1/(1 + 3/(2x)).
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