Simplify $\frac{1+\sqrt{2}}{2+\sqrt{3}}$. Your solution can be converted to the form $A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$ , where $A$, $B$, $C$, and $D$ are positive integers. What is $A+B+C+D$?

A+B+C+D = 13

Step-by-step explanation:

The given expression is:

We have to simply it and express it in the form of:

Multiply and divide the given expression with :

It is the simplified form of given expression.

Formula used:

Comparing the simplified expression with

So, value of

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2