A finished MA 109 Unit 5 rational expressions and equations set: excluded values listed before the working starts and every candidate solution tested against that list. Searches like "ma 109 unit 5 assignment example", "ma109 unit 5 sample" and "ma 109 unit 5 example" land here.
What a finished MA 109 Unit 5 rational expressions and equations looks like
The first line of every item is a restriction statement, not a calculation. It names each denominator, gives the value or values that would make it zero, and marks those as excluded for the rest of the item. Simplification then proceeds with the factored numerator and denominator written out in full, so a reader can see what canceled and confirm that a cancellation removed a common factor rather than a term. Equations take a further stage: the denominators are cleared, the resulting equation is solved with each line shown, and the candidates that emerge are held as candidates until they have been checked. The check is written against the restriction list first and against the original equation second. Each item closes with the solution set stated, and with any rejected candidate named and the reason for rejecting it given.
How a MA 109 Unit 5 example is structured
Restrictions are written before the algebra because the act of clearing denominators destroys the information that produced them, and an item that finds its excluded values afterward is reconstructing something it should never have lost. Factored forms are kept on the page through the cancellation stage so a marker can see that a whole factor left and not a piece of a sum, which is the error this material produces most often. Candidates are called candidates in the writing itself, since naming them solutions before the check has been done is the habit that lets an excluded value survive to the answer line. Two checks are run rather than one because they catch different failures: the restriction list catches a value the equation cannot accept, and substitution catches arithmetic. Rejections are explained instead of quietly dropped, as a marker cannot award a rejection that is invisible.
Excluded values written before any algebra
Each denominator is examined for the values that would make it zero, and those are recorded before the working can erase them.
Factored forms kept through cancellation
Numerator and denominator stay written out in factors so a reader can confirm that a whole factor left rather than part of a sum.
Candidates named as candidates
Values coming out of a cleared equation are labeled as unconfirmed in the writing until both checks have been carried out on them.
Two checks, each catching something different
The restriction list catches a value the original expression cannot accept, and substitution catches an arithmetic slip that the list would miss.
Rejected candidates named with their reason
A discarded value stays on the page with a sentence saying why, because a rejection nobody can see earns nothing.
Where marks go in MA 109 Unit 5
An excluded value reported as a solution is the failure the whole unit is designed to catch, and it costs the item outright rather than partially. Restrictions stated at the end, after the solving, read as an afterthought even when the list is correct, because the point was that they govern the work. Cancellations performed across addition, so that a term rather than a factor disappears, produce a tidy expression that is not equal to the one it came from. Simplified expressions submitted without their domain drop the part that distinguishes this material from ordinary fraction arithmetic. Candidates accepted with no substitution shown leave the check unmarked. Common denominators assembled without the factoring visible give a marker nothing to follow. Answers copied from a solver arrive with the restriction list missing, which is exactly where the credit was.
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MA 109 Unit 5 questions, answered
Why do I lose marks when my answer is right?
Because in this unit the excluded values are part of the answer. An expression simplified correctly, handed in without the domain it came from, is not equivalent to the original and the rubric usually treats that as an incomplete response rather than a formatting matter. The same applies to a solution set that happens to avoid the restrictions by luck: the check has to be visible, not merely satisfied.
Can I use numbers from my own household bills in the applied items?
Where the assignment offers an applied item and leaves the setting open, numbers you gathered yourself are usually welcome and make the work easier to write about. Round them and say they are yours. Keep anything belonging to an employer out of it, and do not present a household figure as a general rate, since the item is about the algebra and a stray claim about costs invites a correction you do not need.
What if none of my candidates survive the check?
Then the equation has no solution and saying so plainly is the correct answer, not a sign that something went wrong. Write the empty solution set, name the candidate that was excluded and the denominator that excluded it, and leave the working above it intact. Sections often include one item like this deliberately, and drafts that keep searching for a value to report usually produce one that cannot be substituted.