multilpying nad dividing rational expressions
I searched Google under the key words "rational expressions multiply divide" to get these possible sources:
http://www.math.csi.cuny.edu/~lewisc/lcm.pdf
http://www.ltcconline.net/greenl/courses/152b/FactoringRatExpr/ratexp.htm
http://www.helpalgebra.com/articles/rationalexpressions.htm
http://www.mathwarehouse.com/algebra/rational-expression/how-to-multiply-divide-rational-expressions.php
http://www.algebra-online.com/dividing-rational-expressions-1.htm
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
To multiply and divide rational expressions, you need to follow a few steps. Let's go through each operation separately:
Multiplying Rational Expressions:
1. Simplify both numerator and denominator if possible by factoring out common factors.
2. Multiply the numerators together to get the final numerator of the result.
3. Multiply the denominators together to get the final denominator of the result.
4. Simplify the result if possible by canceling out any common factors.
For example, let's say you have the following expression:
(a + 2)/(b - 3) * (c - 4)/(d + 5)
To multiply these two rational expressions together, you will proceed as follows:
1. Simplify further if possible (in this case, no further simplification is needed).
2. Multiply the numerators: (a + 2) * (c - 4) = ac - 4a + 2c - 8.
3. Multiply the denominators: (b - 3) * (d + 5) = bd + 5b - 3d - 15.
4. Combine the new numerator and denominator to get the final result:
(ac - 4a + 2c - 8)/(bd + 5b - 3d - 15)
Dividing Rational Expressions:
To divide rational expressions, you can use a similar approach. Instead of multiplying, you will invert (or reciprocate) the second expression and then multiply:
1. Simplify both numerator and denominator if possible by factoring out common factors.
2. Invert (reciprocate) the second expression by swapping the numerator and denominator.
3. Multiply the first expression by the reciprocal of the second expression.
4. Simplify the result if possible by canceling out any common factors.
Let's consider the same expressions as above for division:
(a + 2)/(b - 3) รท (c - 4)/(d + 5)
To divide these two rational expressions, follow these steps:
1. Simplify further if possible (in this case, no further simplification is needed).
2. Invert the second expression: (c - 4)/(d + 5) becomes (d + 5)/(c - 4).
3. Multiply the first expression by the reciprocal of the second expression:
(a + 2)/(b - 3) * (d + 5)/(c - 4)
4. Proceed to multiply the numerators and denominators as shown in the steps for multiplying rational expressions.
Remember to always simplify the resulting expression at the end, if possible, by canceling out any common factors in the numerator and denominator.