Question

1/x-2a+1/x+2a+8a^2/4a^2x-x^3

Answer 1

Заданное  выражение:
1/х   -  2а  +   1/х   + 2а  + 8а²/4а²х   - х³  = 
= (1/х  + 1/х)  + (-2а  + 2а)   +  (2 *4а²)/(х * 4а²)  - х³  =
=  2/х     +  2/х    -  х³  =
=  4/х    -  х³  =
= (1/х )  * (4 -х³)

Возможный вариант выражения:
1/(х - 2а)   + 1/(х + 2а)    +  8а²/(4а²х  - х³)   =
= 1/(х - 2а)  +  1/(х +2а)   +   8а²/ (-х(х² - 4а²) ) =
= 1/(х - 2а)  +   1/(х +2а)   -   8а²/(х(х-2а)(х +2а)  ) = 
= ( 1*х(х +2а)   + 1*х(х-2а)  - 8а²) /  (х(х² -4а²) ) = 
= (х² + 2ах  + х²  - 2ах  - 8а²)/ (х(х² - 4а²) ) =
=  (2х² - 8а²)  / ( х(х² -4а²)  )  = 
=  (  2(х² - 4а²)  ) /  ( х(х² - 4а² )) = 
=  2/х 

Answer 2

To simplify the expression (1/x - 2a) + (1/x + 2a) + (8a^2 / 4a^2x - x^3), we need to combine like terms and perform any necessary operations.

Step 1: Combine like terms in the first two fractions: (1/x - 2a) + (1/x + 2a) = 1/x + 1/x - 2a + 2a = 2/x

Step 2: Simplify the third term: 8a^2 / 4a^2x - x^3 = 2/x - x^3

Now, we have the simplified expression: 2/x + 2/x - x^3 = 4/x - x^3

So, the final simplified expression is 4/x - x^3.