describe when it is and when it is not necessary to use a common denominator when adding, subtracting, multiplying, and dividing rational expressions.

9514 1404 393

Step-by-step explanation:

For multiplication and division, the denominator of the result is developed as part of the algorithm for performing these operations on rational expressions. For example, ...

  (a/b)(c/d) = (ac)/(bd)

  (a/b)/(c/d) = (ad)/(bc)

It is not necessary to make the operands of these operations have a common denominator before the operations are performed. That being said, in some cases, the division operation can be simplified if the operands do have a common denominator or a common numerator:

  (a/b)/(c/b) = a/c

  (a/b)/(a/c) = c/b

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If the result of addition or subtraction is to be expressed using a single denominator, then the operands must have a common denominator before they can be combined. That denominator can be developed "on the fly" using a suitable formula for the sum or difference, but it is required, nonetheless.

  (a/b) ± (c/d) = (ad ± bc)/(bd)

This formula is equivalent to converting each operand to a common denominator prior to addition/subtraction:

Note that the denominator 'bd' in this case will not be the "least common denominator" if 'b' and 'd' have common factors. Even use of the "least common denominator" is no guarantee that the resulting rational expression will not have factors common to the numerator and denominator.

For example, ...

  5/6 - 1/3 = 5/6 -2/6 = 3/6 = 1/2

The least common denominator is 6, but the difference 3/6 can still be reduced to lower terms.

If we were to use the above difference formula, we would get ...

  5/6 -1/3 = (15 -6)/18 = 9/18 = 1/2

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.