Factorising Help?

Question

Explain to me how to factorise an equation like this:

a+b a-b
----- + -----
a+b a+b

It means basically
(a+b)/(a-b) + (a-b)/(a+b)

Answer 1

You are adding two fractions

They already have the same denominator a + b, so it is just

(a + b) + (a - b)
...............................
a + b

= 2a
............
a + b

Answer 2

(a+b)/(a+b) + (a-b)/(a+b)

When adding or subracting fractions, the denominator has to be equal.

In the case of this problem, both the denominators are equal i.e., they're both (a+b)

Therefore,

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

Upon removal of the braces/brackets, you have -

= a + b + a - b / a + b

The +b and the -b cancel each other out. So, you have

= a + a / a + b

Now, adding the 2 "a"s in the numerator, you get the final answer

= 2a / a + b

Voila : )

Answer 3

As the denominators are the same for both fractions, this question is similar to 2/5 + 1/5 = 3/5. Just add the numerators.

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

Answer 4

you can only add fractions if they have the same denominator. yours do. so:

= (a+b+a-b)/(a+b)
= (2a)/(a+b)
=(2a)/a + (2a)/b
= 2 [ 1 + (a/b)]

Answer 5

This is not written out very clearly!! What is the actual question?

a+ba-b?
Or what?

Answer 6

if it helps, another way of writing it is 2a/(a^2-b^2)....well I think it is....

Answer 7

(a + b) / (a - b) + (a - b) / (a + b)
= ((a + b)² + (a - b)²) / ((a - b).(a + b))
= (a² + 2ab + b² + a² - 2ab + b²) / ((a - b).(a + b))
= (2a² + 2b²) / ((a - b).(a + b))
= 2.(a² + b²) / ((a - b).(a + b))