Simplifying compound fractions

In summary, a compound fraction is a fraction that contains one or more fractions in its numerator or denominator. To simplify a compound fraction, you first simplify each individual fraction in the numerator and denominator, then divide the simplified numerator by the simplified denominator. For example, the compound fraction 2/3 + 3/4 can be simplified to 8/9. Some common mistakes when simplifying compound fractions include forgetting to simplify each individual fraction before dividing, and incorrectly simplifying fractions by cancelling out the wrong numbers. Simplifying compound fractions can be useful in various mathematical calculations and can make fractions easier to understand and compare.
  • #1
datafiend
31
0
Hi all,
I'm having a problem simplifying this:

[1/(1+x+h) - 1/(1+x)] / h

How do you get the common denominators for the top 2 fractions?

Thanks
 
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  • #2
Maybe try to find a common denominator for 1+x+h and 1+x.

$(1+x+h)\times(1+h) = x^2+x(2+h)+1+h$
 
Last edited:
  • #3
In the numerator, I would use:

\(\displaystyle \frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}\)
 
  • #4
mark,
thanks again!
 
  • #5
for reaching out and sharing your problem. Simplifying compound fractions can be a bit tricky, but there are a few steps you can follow to make it easier.

First, let's focus on the top two fractions: 1/(1+x+h) and 1/(1+x). In order to add or subtract fractions, they need to have the same denominator. To get the common denominator, you can multiply the denominators of the two fractions together. In this case, the common denominator would be (1+x+h)(1+x).

Next, you need to adjust the numerators of the fractions to match the new denominator. For the first fraction, you would multiply the numerator by (1+x) and for the second fraction, you would multiply the numerator by (1+x+h). This would give you the following fractions: (1+x)/(1+x)(1+x+h) and (1+x+h)/(1+x)(1+x+h).

Now that the fractions have the same denominator, you can combine them by adding or subtracting the numerators. In this case, it would be (1+x) - (1+x+h) = 1 - h.

Finally, you can simplify the resulting fraction by factoring out the common factor of h, leaving you with:

(1 - h)/h

I hope this helps you simplify your compound fraction. If you need further assistance, don't hesitate to reach out to a math tutor or your teacher for additional support. Keep up the good work in your studies!
 

FAQ: Simplifying compound fractions

What is a compound fraction?

A compound fraction is a fraction that contains one or more fractions in its numerator or denominator.

How do you simplify a compound fraction?

To simplify a compound fraction, we first simplify each individual fraction in the numerator and denominator, then divide the simplified numerator by the simplified denominator.

Can you provide an example of simplifying a compound fraction?

For example, let's simplify the compound fraction 2/3 + 3/4. First, we simplify 2/3 to get 2/3. Then, we simplify 3/4 to get 3/4. Finally, we divide 2/3 by 3/4 to get 8/9.

What are some common mistakes when simplifying compound fractions?

Some common mistakes include forgetting to simplify each individual fraction before dividing, and incorrectly simplifying fractions by cancelling out the wrong numbers.

How can simplifying compound fractions be useful?

Simplifying compound fractions can be useful in various mathematical calculations, such as when solving equations or working with proportions. It can also make fractions easier to understand and compare.

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