Factorising Quadratics?

Question

At present I am learning factorising, but aren't really getting the jist of it. This is one of the questions I have been given:

1/a + 1/b = b+a/ab - I would have thought it was (2/ab), being both sides added together...

Also, (3/n+1) + (5/n+1) = (8n+11)/(n^3+3n+2)

Could someone please show me how to do the above questions, as I do not see how these equations are solved?

Answer 1

answers:

(b+a)/2a

8/(n+1)

**************************************...

How:

multiply the "tops" by ab

ab*(1/a+1/b)=

(ab/a) +(ab/b)= "b+a but also=(b/1)+(a/1)

b/1+a/1

multiply the "bottoms" by ab

=

b/ab+a/ab since the "bottoms" are the same now:

add the "tops"

(b+a)/ab

**************************************...

with: 3/ (3/n+1) + 5/(n+1) the bottoms are the same!

so,

add the tops

8/(n+1)

I hope you see the trick.

It's called finding the common denominator "bottom"

Answer 2

First of all, you must be more careful with parentheses:

1/a + 1/b = (b+a)/ab

You are adding fractions. But to add fractions you must first manipulate them so they all have the same denominator. To do this, multiply through:

(ab/ab)(1/a + 1/b) = (b+a)/ab

You can do this because ab/ab = 1.

As for the second equation, it doesn't make sense. (3/n+1) + (5/n+1) = 8/n + 2.

And if what you really meant was 3/(n+1) + 5/(n+1), the sum is 8/(n+1), and not the complicated expression you have on the RHS.