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Bot GPT 3.5 1) Simplify the rational expression: (10x^2 - 25x) / (8x)
To simplify the expression, we can factor out a common term from the numerator:
(10x^2 - 25x) = 5x(2x - 5)
Now, rewrite the expression with the factored form:
(5x(2x - 5)) / (8x)
Next, cancel out the common term "x":
5(2x - 5) / 8
The simplified rational expression is: (5(2x - 5)) / 8
2) Divide: (3/4) ÷ (2/3)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 2/3 = 3/2
Now, multiply: (3/4) * (3/2)
Multiply the numerators: 3 * 3 = 9
Multiply the denominators: 4 * 2 = 8
The result is: 9/8
3) Multiply: (-2/3) * (5/7)
To multiply fractions, multiply the numerators together and the denominators together.
Multiply the numerators: -2 * 5 = -10
Multiply the denominators: 3 * 7 = 21
The result is: -10/21
4) Divide: (5/6) ÷ (-2/5)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of -2/5 = -5/2
Now, multiply: (5/6) * (-5/2)
Multiply the numerators: 5 * -5 = -25
Multiply the denominators: 6 * 2 = 12
The result is: -25/12
5) Simplify the rational expression: (3x^2 - 5x + 2) / (6x^2 - 7x + 2)
To simplify the expression, we can factor the numerator and denominator:
Numerator: 3x^2 - 5x + 2
= (3x - 2)(x - 1)
Denominator: 6x^2 - 7x + 2
= (3x - 2)(2x - 1)
Now, rewrite the expression with the factored form:
((3x - 2)(x - 1)) / ((3x - 2)(2x - 1))
Cancel out the common terms:
3x - 2 / 2x - 1
The simplified rational expression is: (3x - 2) / (2x - 1)
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