How Do You Simplify Complex Fractions with Different Denominators?

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In summary, a fraction is a number that represents a part of a whole and is written in the form of a numerator over a denominator. To simplify a fraction, the greatest common factor of the numerator and denominator must be found and then divided by it. A proper fraction has a smaller numerator than denominator, while an improper fraction has a numerator equal to or greater than the denominator. To convert a fraction to a decimal, divide the numerator by the denominator using long division and round if necessary. A mixed number is a combination of a whole number and a proper fraction written with a space in between.
  • #1
AznBoi
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Here is the fraction that I don't know how to combine and simplify, please help me out! Thanks! =]

[tex]\frac{5}{a} + \frac{4}{2a-6} + \frac {-4a}{a^{2}-9}[/tex]

I found the common denominator I think: (x+3)(x-3) .. but how do you make {a} in that form?
 
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  • #2
If I write it as [tex]\frac{5}{a}+\frac{2}{(a-3)}-\frac{4a}{(a+3)(a-3)}[/tex] does it help?
 
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  • #3
Ok, I didn't see the bit you'd edited. The common denominator will be a(a+3)(a-3).
 
  • #4
oh ok, I knew there wasn't a way to make {a} into {(a+3)(a-3)}. Thanks for your help! =]
 
  • #5
You're very welcome!
 

FAQ: How Do You Simplify Complex Fractions with Different Denominators?

What is a fraction?

A fraction is a number that represents a part of a whole. It is written in the form of a numerator (top number) over a denominator (bottom number). For example, in the fraction 3/4, the numerator is 3 and the denominator is 4.

How do I simplify a fraction?

To simplify a fraction, you need to find the greatest common factor (GCF) of the numerator and denominator. Then, divide both the numerator and denominator by the GCF. The resulting fraction will be in its simplest form.

What is the difference between a proper and improper fraction?

A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is a fraction where the numerator is equal to or greater than the denominator. For example, 3/4 is a proper fraction, while 7/4 is an improper fraction.

How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator by the denominator using long division. If the decimal does not terminate, you can round it to a certain number of decimal places. For example, 3/4 is equal to 0.75 when converted to a decimal.

What is a mixed number?

A mixed number is a combination of a whole number and a proper fraction. It is written in the form of a whole number followed by a space and a proper fraction. For example, 2 1/3 is a mixed number.

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