Question

(a+1/2a-1+6/2a^2-2-a+3/2a+2)*4a^2-4/3​

Answer 1

Ответ:

(a+1)/[2(a-1)]+6/[2(a-1)(a+1)]-(a+3)/[2(a+1)]=

=(a²+2a+1+6-a²-3a+a+3)/[2(a-1)(a+1)]=10/[2(a²-1)]=5/(a²-1)

2)5/(a²-1)*4(a²-1)/3=20/3=6 2/3

Пошаговое объяснение:

вот так

Answer 2

It looks like you've provided a mathematical expression, and I'll be happy to help you simplify it:

The given expression is:

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(a + 1) / (2a - 1) + (6 / 2a^2 - 2 - a + 3) / (2a + 2) * (4a^2 - 4/3)

Let's break down the steps:

1. Simplify the fractions inside the parentheses.
2. Distribute the second fraction with the expression (4a^2 - 4/3).

Starting with step 1:

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(a + 1) / (2a - 1) + (6 / 2a^2 - 2 - a + 3) / (2a + 2)

Now let's find a common denominator for both fractions inside the parentheses. The common denominator for the first fraction is (2a - 1) * (2a + 2) and for the second fraction is (2a + 2) * (2a - 1).

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((a + 1) * (2a + 2)) / ((2a - 1) * (2a + 2))
+ ((6 / (2a^2)) - (2 - a + 3) * (2a - 1)) / ((2a + 2) * (2a - 1))

Now let's simplify the fractions inside the parentheses:

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(2a^2 + 2a + 2a + 2) / (4a^2 - 1)
+ ((6 / (2a^2)) - (2a - 2 - a + 3) * (2a - 1)) / (4a^2 - 1)

Simplify the numerators further:

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(4a^2 + 4a + 2) / (4a^2 - 1)
+ (6 / (2a^2) - (4a^2 - 3a + 1) * (2a - 1)) / (4a^2 - 1)

Now, let's work on the second fraction in the expression:

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6 / (2a^2) - (4a^2 - 3a + 1) * (2a - 1)

Distribute the -1 through the second term in the parentheses:

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6 / (2a^2) - (8a^3 - 6a^2 + 2a - 4a^2 + 3a - 1)

Combine like terms in the second term:

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6 / (2a^2) - (8a^3 - 10a^2 + 5a - 1)

Now, bring this result back to the main expression:

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(4a^2 + 4a + 2) / (4a^2 - 1)
+ (6 / (2a^2) - (8a^3 - 10a^2 + 5a - 1)) / (4a^2 - 1)

Continuing to simplify the fractions:

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(4a^2 + 4a + 2) / (4a^2 - 1)
+ (6 / (2a^2) - 8a^3 + 10a^2 - 5a + 1) / (4a^2 - 1)

Combining the fractions:

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(4a^2 + 4a + 2 + 6 - 8a^3 + 10a^2 - 5a + 1) / (4a^2 - 1)

Simplifying the numerator:

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(14a^2 - 1 - 8a^3 + 5a + 6) / (4a^2 - 1)

Combining like terms:

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(-8a^3 + 14a^2 + 5a + 5) / (4a^2 - 1)

So, the simplified expression is:

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(-8a^3 + 14a^2 + 5a + 5) / (4a^2 - 1)

Please double-check my steps and calculations to ensure accuracy.