SOLUTION: Adding and Subtracting Radical Expressions: Perform the operation and Simplify. {{{ (5)/(x+y) }}} + {{{ (5)/(x^2-y^2) }}}

Question 72429: Adding and Subtracting Radical Expressions:
Perform the operation and Simplify.
+

Found 2 solutions by Cintchr, bucky:
Answer by Cintchr(481) (Show Source): You can put this solution on YOUR website!
You must have common denominators.
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Factor the second denominator
+
Multiply the first fraction by (x-y)/(x-y)
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Distribute the 5 in the first numerator
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Combine the two fractions by adding the numerators

You can factor out a 5 from the numerator if your instructor wants you so go that far

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
To simplify this expression, you can first note that is the difference
of two squares. Therefore, it factors into . Substitute these and
the problem becomes:
.

.
Notice that the first fraction lacks a (x-y) term in the denominator. If it had one, then
this first fraction could be combined with the second fraction because they both would have
the same denominator.
.
Let's multiply the first fraction by . Because the numerator is identical to
the denominator in this multiplier, it is equivalent to multiplying by 1. The multiplication
results in:
.

.
Since the two fractions now have a common denominator of their numerators
may be put over this common denominator to get:
.

.
Then, doing the multiplication in the numerator results in:
.

.
And factoring the common 5 in the numerator:
.

.
Hope this gives you some additional insight into working with fractional expressions.
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