SOLUTION: In this discussion, you are assigned two rational expressions with which you will then do a variety of math work. Remember that each polynomial must be fully factored and that you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: In this discussion, you are assigned two rational expressions with which you will then do a variety of math work. Remember that each polynomial must be fully factored and that you       Log On


   

Question 597723: In this discussion, you are assigned two rational expressions with which you will then do a variety of math work. Remember that each polynomial must be fully factored and that you can only cancel factors; you cannot cancel terms. Read the following instructions in order and view the example to complete this discussion:
Find your two rational expressions in the list below based on your first initial.
k^2+k-42/1-k and k^2-k-30/k-1
Find the domain of each of the rational expressions. (Identify which values of x will make the denominator zero and thus are not allowed in the domain.)
Divide your first rational expression by the second one. Write the answer in lowest terms.
Find and state the common denominator between the two expressions. Build up each expression so that it has the common denominator. (Remember not to do any canceling at this point since you need those extra factors for the common denominator.)
Add the two rational expressions together. Factor again if possible, and present the answer in lowest terms.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
Domain
Lowest terms
Opposites
LCD
Build up
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe that
%28k%5E2%2Bk-42%29%2F%281-k%29=(k^2+k-42)/(1-k) and %28k%5E2-k-30%29%2F%28k-1%29=(k^2-k-30)/(k-1) are your expressions for this problem.
When you cannot type a horizontal line sandwiched between polynomials, you need those parentheses.

A NOTE ABOUT ORDER OF OPERATIONS:
Without those parentheses, the meaning is different
k^2+k-42/1-k=k%5E2%2Bk-42%2F1-k=k%5E2%2Bk-42-k=k%5E2-42
Otherwise, some people may understand what you meant. However, other people, along with all computers and calculators, will not know what you meant, and you will end up with the wrong result. I've seen that happen to chemists hastily calculating the results of an analysis.

THE DOMAIN is the same for those two rational expressions. Only one value of x (x=1) will make the denominator zero and thus is not allowed in the domain.

DIVIDING RATIONAL EXPRESSIONS
%28%28%28k%5E2%2Bk-42%29%2F%281-k%29%29%29%2F%28%28%28k%5E2-k-30%29%2F%28k-1%29%29%29=%28%28k%5E2%2Bk-42%29%2F%281-k%29%29/%28%28k%5E2-k-30%29%2F%28k-1%29%29=%28%28k%5E2%2Bk-42%29%2F%281-k%29%29%2A%28%28k-1%29%2F%28k%5E2-k-30%29%29=%28%28k%2B7%29%28k-6%29%2F%28-1%28k-1%29%29%29%2A%28%28k-1%29%2F%28k-6%29%28k%2B5%29%29=%28k%2B7%29%28k-6%29%28k-1%29%2F%28%28-1%29%28k-1%29%28k-6%29%28k%2B5%29%29
At this point, your teacher may expect you to do this:

or something similar.
Some teacher may prefer

or something similar.
Canceling all pairs of identical factors present in numerator and denominator of a rational expression yields an equivalent rational expression IN LOWEST TERMS.

COMMON DENOMINATOR AND ADDITION:

In the first step, numerator and denominator of the first rational expression were multiplied by (-1) to BUILD UP the expression so that both expressions would have the common denominator.
The terms -k%5E2 and k%5E2 are OPPOSITES and so they add to yield zero.