Let us start this
I tried just shoving this one into Microsoft Math Calc so I can steer the right path and go to sleep tomorrow but it kept throwing an error. I tried a few different ways but nothing. So then I stuck it in the GPT 3.5 Broiler and...
To simplify the expression ((2/x²) + 4)/((2/x²) - (2/3x)), follow these steps:
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Find a Common Denominator: To simplify this complex fraction, find a common denominator for the fractions in the numerator and denominator. In this case, the common denominator is x² * 3x, which is the least common multiple (LCM) of the denominators.
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Convert to a Single Fraction: Rewrite the complex fraction as a single fraction with the common denominator:
[(2 * 3x + 4 * x²) / (x² * 3x)] / [(2 * 3x - 2 * x²) / (x² * 3x)]
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Simplify the Numerator and Denominator: Simplify the fractions in the numerator and denominator:
Numerator: 6x + 4x² Denominator: 6x - 2x²
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Combine the Fractions: Combine the fractions:
(6x + 4x²) / (6x - 2x²)
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Factor and Cancel Common Factors: Factor common terms from the numerator and denominator and cancel any common factors:
(2x(3 + 2x)) / (2x(3 - x))
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Final Simplification: The expression is now simplified as:
(3 + 2x) / (3 - x)
So, the simplified form of the expression ((2/x²) + 4)/((2/x²) - (2/3x)) is (3 + 2x) / (3 - x).
UNFILTERED GPT GENIUS. I am pretty sure GPT has an issue with spacing. This time, when I copy pasted their first fractions into Microsoft math, the power of 2 was applied to the fraction itself and not to x.
WE R
STILL WRONG KEEP TRYING
