There are a couple ways to go about solving this problem. One could simply take the reciprocal of the second fraction, multiply everything out, and then look for ways to simplify. However, it is almost always easier to simplify before doing any multiplying.

To begin, we need to take the reciprocal of the second fraction, so that our expression becomes:

Then, before we multiply anything out, try to factor out the different parts of this expression. If we have any common factors in the numerator and denominator, we can cancel them out. In this case, the above expression factors as follows:

Conveniently, we can cancel out a bunch of factors here!

The common factors are highlighted in corresponding colors. We can actually cancel everything out here. We have a  in both the numerator and the denominator, and also an  term. We also have two  terms in both the numerator and the denominator, so all of these terms will cancel, and we will be left with :

The reason we can cancel out terms when they are in the numerator and denominator is that we are essentially multiplying and then dividing by the same term. Since multiplication and division are opposite operations, they cancel each other out and we are left with .

Important side note: you can only cancel across two different fractions when you are multiplying and/or dividing. You CANNOT cancel factors across fractions if you are adding or subtracting them.

The easy way to solve this problem is to multiply both halves of the fraction by the conjugate of the denominator, since this will eliminate the radical in the denominator.

 Conjugate the fraction.

Next, simplify the denominator, eliminating any terms you can along the way.

Thus,  is our answer.

The easy way to solve this problem is to multiply both halves of the fraction by the conjugate of the denominator, since this will eliminate the radical in the denominator.

 Conjugate the fraction.

Next, simplify the fraction, eliminating any terms you can along the way.

Thus,  is our answer.

The easy way to solve this problem is to multiply both halves of the fraction by the conjugate of the denominator, since this will eliminate the radical in the denominator.

 Conjugate the fraction.

Next, simplify the fraction, eliminating any terms you can along the way.

Thus,  is our answer.

To begin, factor out the greatest common factor from each of the binomials to check for compatibility:

 Factor.

Next, eliminate the common factors and simplify.

 Eliminate and simplify.

Lastly, clean up the fraction.

Thus, our answer is .

To begin, factor out the greatest common factor from each of the binomials to check for compatibility:

 Factor.

Next, eliminate the common factors and simplify.

 Eliminate and simplify.

Lastly, clean up the fraction.

Thus, our answer is .

This problem looks intimidating, but can be solved with our standard tool; factoring the GCF out of each binomial.

Eliminate the obvious binomial:

But we're not through yet! Notice that we can further simplify this fraction:

Eliminate another pair, and the solution is now obvious:

Thus, our answer is .

When multiplying two binomials, it's best to remember the mnemonic FOIL, which stands for First, Outer, Inner, and Last. Going in the order of FOIL, we multiply the first term of each binomial, then the outer terms of the expression, then the inner terms of the expression, and finally the last term of each binomial. For this question we get:  Now that we have 'FOILed' our expression, we simply add our results to get the final answer. 

Use cross-cancellation as follows:

Factor the numerator and denominator in the second fraction, cross-cancel common factors, then multiply out.