Reduce the following rational expression to the lowest form
1 answer:
Answer:
4x(x - 1)
Step-by-step explanation:
Factor the numerator and denominator
64 - 64x ← factor out 64x from both terms
= 64x( - 1) ← difference of squares
= 64x(x² - 1)(x² + 1) ← x² - 1 is also a difference of squares
= 64x(x - 1)(x + 1)(x² + 1)
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(8x² + 8)(2x + 2) ← factor out 8 and 2 from each factor
= 8(x² + 1) × 2(x + 1)
= 16(x² + 1)(x + 1)
Then expression can be written as
← cancel (x² + 1) and (x + 1) on numerator/ denominator
= ← cancel common factor 16 on numerator/ denominator
= 4x(x - 1)
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Answer:
B has the greatest range for a given amount of fuel
Step-by-step explanation:
In the US, fuel efficiency is measured in terms of miles per gallon. This value is found by dividing the number of miles traveled by the corresponding number of gallons used.
When calculations are repetitive, it is often useful to use a spreadsheet to do them. You can enter the formula once, and have it operate on all the different data sets. Here, the formula divides the number in the miles column (range) by the number on the same row in the gallons column (fuel).
We find the greatest miles per gallon (best efficiency) is given by Option B.
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<em>Additional comment</em>
Many places in the world measure fuel efficiency by the amount of fuel required to deliver a certain outcome. In this problem, that would be expressed as gallons per some number of miles, perhaps 100 miles. Using that measure, a lower value indicates better performance.
