Simplify:
this is a triple decker fraction
1/a + 1/c divided by
a^2 - c^2 divided by
ac
I am stuck on this one please help.
The answer depends upon which division is done first. For example:
(a/b)/c = a/(bc), but
a/(b/c) = ca/b
They are NOT the same.
You need to clarify the sequence of operations
If you write 1/a + 1/c as (a+c)/ac, and a^2 - c^2 = (a+c)(a-c)
you can get some cancellations and simplify the expression.
I am not sure how else to put this one on this forum to clarify the sequence, so thank you for your help
To simplify the given expression, let's break it down step by step.
Step 1: Simplify the numerator
The numerator is the expression 1/a + 1/c. To add these fractions together, you need a common denominator. In this case, the common denominator is ac. So, we can rewrite the expression as (c + a) / (ac).
Step 2: Simplify the denominator
The denominator is the expression (a^2 - c^2) / ac. Notice that the numerator is the difference of squares: a^2 - c^2 = (a - c)(a + c). Therefore, we can rewrite the denominator as [(a - c)(a + c)] / ac.
Step 3: Divide
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have (c + a) / (ac) divided by [(a - c)(a + c)] / ac. Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the expression as:
(c + a) / (ac) * (ac) / [(a - c)(a + c)]
Step 4: Cancel out common factors
In the numerator, the ac in the first fraction cancels out with the ac in the second fraction. Also, in the denominator, the (a + c) cancels out with the (a + c) from the first fraction, and the (a - c) cancels out with the (a - c) in the second fraction. This leaves us with:
(c + a) / (a - c)
Overall, the simplified expression is (c + a) / (a - c).
Keep in mind that this is a general explanation of how to simplify the given expression. If you have specific values for 'a' and 'c', you can substitute those in and perform any additional simplification necessary.