How do I simplify this?

Question

the problem is 2a/a+b - 3b/a-b

(its for a study guide for a test I've already passed...haha)

Answer 1

Get the LCD:

2a/a+b - 3b/a-b

= [2a(a-b) - 3b(a+b)]/(a^2 - b^2)

Distribute.

= [2a^2 -2ab -3ab - 3b^2]/(a^2 - b^2)

= [2a^2 - 5ab - 3b^2]/(a^2 - b^2)

Answer 2

= (2a/[a + b]) - (3b/[a - b])

= ([2a² - 2ab] - [3ab + 3b²])/([a + b][a - b])

= (2a² - 2ab - 3ab - 3b²)/([a + b][a - b])

= (2a² - 5ab - 3b²)/([a + b][a - b])

= ([2a - 3b][a - b])/([a + b][a - b])

= (2a - 3b)/(a + b)

Answer: (2a - 3b)/(a + b)

Answer 3

That depends. Without parentheses, the best I can tell is that you want to simplify this:

(2a/a) + b - (3b/a) -b

Then the +b and -b cancel, the 2a/a simplifies to a, and you get a-3b/a. To simplify, put them both over a to get:

(a^2-3b)/a

Or, if you meant:

2a/(a+b) - 3b/(a-b)

Put them over the common denominator of (a+b)(a-b) to get:

[2a(a-b) - 3b(a+b)]/[(a+b)(a-b)] =

[2a^2 - 2ab - 3ab - 3b^2]/[a^2 - b^2] =

(2a^2 - 5ab - 3b^2)/(a^2 - b^2)

-IMP ;) :)  

Answer 4

Well since both 2a and 3b are over a-b I am pretty sure that it would only be 2a-3b/a-b