When multiplying fractions, find a way to reduce any of the fractions before multplying them out.

For example, sinceis a multiple of, you would cancel out theand that becomes aand thebecomes a.

The same goes forand. Thebecomesand thegoes to.

Overall, the fractions to multiply becomes

. Answer should be.

is not correct because it's not reduced.

We need to get rid of that denominator to solve this problem easily.

Multiply top and bottom by the reciprocal of the denominator or.

这should leave you with.

Now, find a way to reduce any of the fractions before multplying them out.

For example, sinceis a multiple of, you would cancel out theand that becomes aand thebecomes a.

The same goes forand. Thebecomesand thegoes to.

这leaves you with. Answer is.

is not simplified.

这involves a lot of dividing exponents with same base. When dividing exponents of the same base, all you have to do is take the exponent from the numerator and subtract it with the denominator.

For example, with the same base,, the numerator has aand denominator is. Take the diference which is. Same appliesand. Since their differences are negative, it means there were morandin the denominators.

So far, the overall fraction is.

divides into,times.

Now with that simplification, answer is shown.

Always look to reduce fractions. Thewill cancel out from the denominator of left fraction with numerator of right fraction.

这leads to

.

Now, multiply numerator with numerator and denominator with denominator.

Remember the distribute thein the denominator which leads you to the answer.

Take care of the exponents first before solving the problem.

The numerator should beand denominator is.

Then theshould cancel out leaving you with the right answer.

Don't try to multiply everything out. Try to factor all the quadratics out into simple binomials. Remember, we need two numbers who are factors of the c term must add up the value of the b term.

With that, the fraction now looks like:

.

The,, andall cancel leaving you withas the final answer.

First, let's take care of the exponents. When dividing exponents of the same base, all you have to do is take the exponent from the numerator and subtract it with the denominator. Now we haveleftover in the numerator.

Let's take a look at the denominator of the left fraction. It may not be obvious but if you factor out, we are left with an expression:. We have ain the numerator so now they can cancel out.

Lastly, lets focus on the quadratic in the denominator. Does it look familiar? It is. The numerator in the right fraction has.

Same rule applies with dividing exponents.

这should leave you with justas the final answer.

There are two methods in solving this problem.

Method 1:

Try to simplify the problem as best as you can before you cross-multiply. Remember when breaking down the quadratic, find two terms which are factors of the c term that are also the sum of the b term. The equation should be:

.

Thecancel out and now we can cross-multiply. This new equation is now. Distribute theand have like-terms on one side of the equation and the rest on the otherside of the equation. Answer should be.

Method 2 (Not preferred):

If you don't know how to simplify the equation, that's ok. Lets just cross-multiply and create a quadratic equation.

We can plug into quadratic equation, or factor. Regardless, we should have:.

解决个人:

WAIT, how come answer isn't Bothand. The reason this method is not preferred is because many people forget we need to check if these answers are valid with the original question. We will use the factored equation from method 1:. Remember, if at any point a denominator is, the fraction is undefined. From the denominator, ifwas eitheror(二次)的根,压裂tion is undefined. Since we have an answer ofand that's one of the values that makes the fraction undefined, we cross that out as a possible answer which leaves onlyas the only possible answer. If you plug inback into the question we get:

这answer is valid and correct.

Don't try to multiply both numerators and denominators and cross-multiply. It will be time-consuming and too much work. Instead, lets try to simplify. Lets factor the denominator of the left fraction by taking out a. We now have:

Theandcancel out leaving abehind. If you don't believe it, just plug in any value forsay. One answer gives you, anotherThe relationship between these values is ratio is. With that simplification, lets cross-multiply:

Divide both sides by:

Take the square root of both sides and remember when doing that, you need to account for the negative value of the root. This should lead you to two possible answers. There is no answer ofHOWEVER, to get the right answer, break the radical into:

and multiply top and bottom byto get the right answer,.

First, lets factor and reduce some terms. Remember, we need to find two terms that are factors of the c term that add up to the b term. This should look like this:

Remember, order of operations is crucial. *PEMDAS* Multiplication has priority over addition. So when cancelling, we should only have:

这should be simple with both fractions having the same denominator. We now have:

. Then cross-multiply.

Then subtracton both sides to get the answer.

Make sure this value doesn't violate any undefined fraction. As you check, this answer is still good and is the right answer.