Simplifying compound fractions

[datafiend]

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

 

[pickslides]

Maybe try to find a common denominator for 1+x+h and 1+x.

$(1+x+h)\times(1+h) = x^2+x(2+h)+1+h$

 

[MarkFL]

In the numerator, I would use:

\(\displaystyle \frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}\)

 

[datafiend]

mark,
thanks again!

 

[CellCoree]

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!