Question

prove that a+b/a + a+b/b = (a+b/a)(a+b/b)​

Answer 1

Step-by-step explanation:

Yes, but the proof depends on what your axioms are. In other words, it depends on where you want to start. Let’s start rather far out. That is, let’s assume we have a set of objects, i.e., numbers, along with a binary operation, i.e., addition, which obey the following properties:

a+b=b+aa+b=b+a (commutative property),

a+(b+c)=(a+b)+ca+(b+c)=(a+b)+c (associative property),

a+0=aa+0=a (existence and uniqueness of the identity element),

−a+a=0−a+a=0 (existence of inverses).

The first two properties are probably familiar. The third one states that there exists exactly one number, namely 00 , which preserves identity when added to any number. The fourth property states that every number has an inverse, meaning that a number plus its inverse is 00 (the identity element). Note that the minus sign here is just notation. That is −a−a just means the inverse of aa .

From the third property above, we have:

0+0=0.0+0=0.

Using the fourth property above, let’s replace each 0 on the left with a number plus its inverse:

(−a+a)+(−b+b)=0(−a+a)+(−b+b)=0 .

Using the first and second properties above, we can rewrite this as:

((−a)+(−b))+(a+b)=0((−a)+(−b))+(a+b)=0 .

Note that the inverse of a+ba+b is −(a+b)−(a+b) . (Recall that the minus sign is just notation for inverse.) So, by once again using the fourth property above, as well as the uniqueness of 00 , the two terms on the left must be inverses of each other. That is,

((−a)+(−b))=−(a+b)((−a)+(−b))=−(a+b) .

Answer 2

Answer:

have a great day dear

Step-by-step explanation:

hope you're well