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Since exponents of 1/2 mean the same thing as square roots, I am going to rewrite the expression with square roots:
Next we will simplify each square root. Part of simplifying square roots is rationalizing the denominators. There are a variety of ways to go about doing this. I like to start by making each denominator a perfect square:
which leads to:
Next we use the property of radicals to split each square root:
Because of our earlier work, each denominator will simplify:
Next we simplify the square roots in the numerators. Each one happens to have one or more prefect square factors (which I like to put first using the Commutative Property of Multiplication):
Now we use another property of radicals, , to split the square roots so that each perfect square factor is in its own square root:
Each of the square roots of the perfect squares simplify:
which simplifies further to:
The last two fractions reduce:
And last of all, these are all like terms! They are all terms. So we can add/subtract them. Just add/subtract the coefficients. To see this more easily, I'm going to rewrite the first and third terms so we can see the coefficient we should add:
which simplifies to:
since
So
simplifies to
or, if you prefer the 1/2 exponents:
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