Problem solving involving rational algebraic expression. Equations Involving Rational Expressions Examples

Here is the least common denominator for this rational expression. Now what does it say about the time in the problem? Since our answer is not 0, the answer is accepted. Note as well that the numerator of the second rational expression will be zero.

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    So let's write that in under rate. You're losing speed because you have to fight the current.

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    • So it would be a minus.

    Note as well that to do division of rational expressions all that we need to do is multiply the numerator by the reciprocal of the denominator i. Eliminate all fractions. Recall that in order to cancel a factor it must multiply the whole numerator and the whole denominator.

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    That example was also an instance of a proportion, which is an equation that says two ratios are equal. In particular, they are quite good for describing distance-speed-time relationships and for modeling work problems that involve more than one person.

    We now need to move into adding, subtracting, multiplying and dividing rational expressions. Now we can go ahead and solve this sucker.

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    Substitute each solution into the denominator of the original question and reject any solutions that cause the denominator to equal zero because this makes the problem undefined. Polynomials often appear in problems where one quantity depends on another.

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    Since our answer is 4, the answer is not accepted, which means: When solving word problems involving polynomials or rational expressions, make sure that you only keep those solutions that make sense in the context of the word problem.

    Before writing down our final answers, we need to make sure 0 and aren't "bad" values. In this case, we need to get the equation equal to zero and solve by factoring.

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    Show Next Step. One way of solving rational equations with unlike denominators is to multiply both sides of the equation by the least common multiple of the denominators of all the fractions contained in the equation.

    First, factor:

    In the last term recall that we need to do the multiplication prior to distributing the 3 through the parenthesis. When dealing with numbers we know that division by zero is not allowed.

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    Notice that we moved the minus sign from the denominator to the front of the rational expression in the final form. We can set this up as a proportion: Slaps forehead with palm.

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    Our two solutions are not, in fact, "bad" answers, so our final answers are: This step does not guarantee that the answer is correct; it only guarantees that the answer is acceptable. The problem states: If the area covered by the blanket is 28 square feet, how long is the blanket?

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    The length of the blanket is: So we will write both of those down and then take the highest power for each.