Question

1) a^2+b^2/a-b - a= 2) 1/p-q-3pq/p^3-q^2= 3) a/a-6 - 3/a-6 + a^2/36-a^2=

Answer 1

Ответ:.............................

Answer 2

Let's simplify each of the expressions step by step:

1. a^2 + b^2 / (a - b) - a

To simplify this expression, we need to find a common denominator for the fractions and then combine like terms.

Common denominator: (a - b)

a^2 + (b^2 - a(a - b)) / (a - b)

Expand the numerator:

a^2 + (b^2 - a^2 + ab) / (a - b)

Combine like terms in the numerator:

b^2 + ab / (a - b)

Factor out 'b' from the numerator:

b(a + b) / (a - b)

Final simplified expression:

b(a + b) / (a - b)

2. 1 / (p - q) - 3pq / (p^3 - q^2)

To simplify this expression, we need to find a common denominator for the fractions and then combine like terms.

Common denominator: (p^3 - q^2)

(p^3 - q^2) / (p - q) - 3pq / (p^3 - q^2)

Expand the first fraction's numerator:

(p^3 - q^2 - (p^3 - 3pq^2)) / (p^3 - q^2)

Combine like terms in the numerator:

(p^3 - q^2 - p^3 + 3pq^2) / (p^3 - q^2)

Simplify the numerator:

(3pq^2 - q^2) / (p^3 - q^2)

Factor out 'q^2' from the numerator:

q^2(3p - 1) / (p^3 - q^2)

Final simplified expression:

q^2(3p - 1) / (p^3 - q^2)

3. a / (a - 6) - 3 / (a - 6) + a^2 / (36 - a^2)

To simplify this expression, we need to find a common denominator for the fractions and then combine like terms.

Common denominator: (a - 6)(36 - a^2)

a(36 - a^2) / (a - 6)(36 - a^2) - 3(36 - a^2) / (a - 6)(36 - a^2) + a^2(a - 6) / (a - 6)(36 - a^2)

Now, combine the numerators:

(a(36 - a^2) - 3(36 - a^2) + a^2(a - 6)) / (a - 6)(36 - a^2)

Expand and simplify the numerator:

(36a - a^3 - 108 + 3a^2 + a^3 - 6a^2) / (a - 6)(36 - a^2)

Combine like terms in the numerator:

(36a - 6a^2 - 108) / (a - 6)(36 - a^2)

Factor out '6' from the numerator:

6(6a - a^2 - 18) / (a - 6)(36 - a^2)

Final simplified expression:

6(6a - a^2 - 18) / (a - 6)(36 - a^2)

Please double-check the expressions and the steps to ensure accuracy. If you have any further questions or need additional clarifications, feel free to ask!