10/a-5 + 20a/25-a^2 + 2

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вопрос

To simplify this expression, we first need to combine like terms:

10/(a-5) + 20a/(25-a^2) + 2

Next, we need to factor the denominator on the second term in order to simplify it further:

25 - a^2 = (5 + a)(5 - a)

Now, we can rewrite the expression with the factored denominator:

10/(a-5) + 20a/[(5 + a)(5 - a)] + 2

Next, we need to find a common denominator for all the terms:

The common denominator is (a-5)(5 + a)(5 - a)

Rewriting each term with the common denominator:

10*(5 + a)(5 - a)/[(a-5)(5 + a)(5 - a)] + 20a(a-5)/[(a-5)(5 + a)(5 - a)] + 2(a-5)(5 + a)/[(a-5)(5 + a)(5 - a)]

Now, we can combine the terms with the common denominator:

[50 + 10a + 10a - 50a]/[(a-5)(5 + a)(5 - a)] + [20a^2 - 100a]/[(a-5)(5 + a)(5 - a)] + [10a - 50 + 10a]/[(a-5)(5 + a)(5 - a)]

Combining like terms in the numerator, we get:

(20a - 50a)/[(a-5)(5 + a)(5 - a)] + (20a^2 - 100a)/[(a-5)(5 + a)(5 - a)] + (20a - 50)/[(a-5)(5 + a)(5 - a)]

Now, simplify the expression further:

-30a/[(a-5)(5 + a)(5 - a)] + (20a^2 - 100a)/[(a-5)(5 + a)(5 - a)] + (20a - 50)/[(a-5)(5 + a)(5 - a)]

We can factor out -10a from the numerator of the first term:

(-30a + 20a^2 - 100a + 20a - 50)/[(a-5)(5 + a)(5 - a)]

Now, combine like terms in the numerator:

(20a^2 - 110a - 50)/[(a-5)(5 + a)(5 - a)]

Therefore, the simplified expression is (20a^2 - 110a - 50)/[(a-5)(5 + a)(5 - a)].