Simplify Fractions: 4x²-6x/(4x²-9)

In summary, the purpose of simplifying fractions is to express them in their most reduced form, making it easier to compare and perform operations. To simplify fractions, one must find the greatest common factor (GCF) and divide both the numerator and denominator by it. This process also applies to fractions with variables, where the variables must be factored first. Simplifying and reducing fractions are essentially the same thing and are used interchangeably. In scientific calculations, it is important to use simplified fractions to avoid errors and make calculations more efficient, as well as to express and compare data in experiments.
  • #1
thomas49th
655
0

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:
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  • #2
Sorry, but where are you getting the 4x^2 from?
 
  • #3
Sorry, I missed it out in the equatio above... I've edited it in now

Thanks
 
  • #4
You can't cancel out the 4x^2 like that! That's an illegal move.
 
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  • #5
You can only cancel out factors! never terms!

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FAQ: Simplify Fractions: 4x²-6x/(4x²-9)

What is the purpose of simplifying fractions?

The purpose of simplifying fractions is to express a fraction in its most reduced form. This makes it easier to compare and perform operations with fractions.

How do you simplify fractions?

To simplify fractions, you need to find the greatest common factor (GCF) of the numerator and denominator, and then divide both by the GCF. This will result in a fraction that cannot be reduced any further.

Can fractions with variables be simplified?

Yes, fractions with variables can be simplified. You would follow the same steps as simplifying fractions with numbers, but you would need to factor the variables first to find the GCF.

What is the difference between simplifying and reducing fractions?

Simplifying and reducing fractions are essentially the same thing. The terms are often used interchangeably, but they both refer to expressing a fraction in its most simplified form.

Why is it important to simplify fractions in scientific calculations?

In scientific calculations, it is important to use simplified fractions to avoid errors and make calculations more efficient. Simplified fractions also make it easier to express and compare data in scientific experiments.

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