Question

Simplify;a/2(a+b)+b/2(a-b)​

Answer 1

`(a)/(2(a+b))+(b)/(2(a-b))=\\\\(a(a-b))/(2(a+b)(a-b))+(b(a+b))/(2(a+b)(a-b))=\\\\(a^2-ab)/(2(a^2-b^2))+(ab+b^2)/(2(a^2-b^2))=\\\\(a^2+b^2)/(2(a^2-b^2))`

Answer 2

`\huge\boxed{\sf (a^2+b^2)/(2(a^2-b^2))}`

Explanation:

=>
`\sf (a)/(2(a+b)) + (b)/(2(a-b))`

LCM = 2(a+b)(a-b)

=>
`\sf (a(a-b)+b(a+b))/(2(a+b)(a-b))`

Simplifying further

=>
`\sf (a^2-ab+ab+b^2)/(2(a^2-b^2))`

=>
`\sf (a^2+b^2)/(2(a^2-b^2))`