Question

Hw assignment:simplify the given expression , im not sure how to do this with all the extra numbers and letters it’s very confusing

Answer 1

Given:

`(x_1+x_2)/(9)/(ea^4x_1^2-ea^4x_2^2)/(81ua)`

Required:

We need to simplify the given expression.

Step-by-step explanation:

`Use\text{ }(a)/(b)/(c)/(d)=(a)/(b)*(d)/(c).`

`(x_1+x_2)/(9)/(ea^4x_1^2-ea^4x_2^2)/(81ua)=(x_1+x_2)/(9)*(81ua)/(ea^4x_1^2-ea^4x_2^2)`

`=(x_1+x_2)/(9)*(81ua)/(ea^4x_1^2-ea^4x_2^2)`

Take the common term out.

`=(x_1+x_2)/(9)*(81ua)/(ea^4(x_1^2-x_2^2))`
`Use\text{ }a^2-b^2=(a-b)(a+b).`

`=(x_1+x_2)/(9)*(81ua)/(ea^4(x_1-x_2)(x_1+x_2))`
`Ca\text{ncel out the common term }(x_1+x_2).`

`=(1)/(9)*(81ua)/(ea^4(x_1-x_2))`

Cancel out the term a.

`=(1)/(9)*(81u)/(ea^3(x_1-x_2))`

Cancel out 9 multiples.

`=(9u)/(ea^3(x_1-x_2))`

Final answer:

`(x_1+x_2)/(9)/(ea^4x_1^2-ea^4x_2^2)/(81ua)=(9u)/(ea^3(x_1-x_2))`