New Problem

[krisolaw]

Perform the operations and simplify when possible:

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

Please show me! Thanks in advance!

 

[tkhunny]

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

Change it to this:

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

The Least Common Denominator should now be obvious.

 

[krisolaw]

Change it to this:

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

The Least Common Denominator should now be obvious.

I have this:
a/(a-b) + b/(a+b) - (a^2 + b^2)/(a +b)(a-b) LCD is now (a +b)(a - b)
[a(a+b) + b(a - b) - (a ^2 + b ^2)]/(a + b)( a - b) then:
(a ^2 + ab + ab - b^2 -a^2 - b^2)/(a + b)(a - b) so combine like terms:
(2ab - 2b^2)/(a +b)(a - b) then:
2b(a-b)/(a+b)(a-b)
answer: 2b/(a+b)

Please check! Thanks again!!!

 

[Denis]

Correct!

By the way, this 2b(a-b)/(a+b)(a-b) needs another set of brackets:
2b(a-b) / [(a+b)(a-b)]

Example:
20/2*5 = 50
20/(2*5) = 2 : quite a difference, hey?