A+2√ab+b÷a-b×a√a-b√b÷a+b+√ab

 [latex] frac{a+2 sqrt{ab}+b }{a-b} * frac{a sqrt{a} -b sqrt{b} }{a+b+ sqrt{ab} } = frac{ ( sqrt{a} + sqrt{b})^{2} }{( sqrt{a} - sqrt{b} )( sqrt{a} + sqrt{b} )} * frac{( sqrt{a} )^{3} -( sqrt{b} ) ^{3} }{a+b+ sqrt{ab} } = \ =frac{ ( sqrt{a} + sqrt{b})^{2} }{( sqrt{a} - sqrt{b} )( sqrt{a} + sqrt{b} )} * frac{( sqrt{a} - sqrt{b} )(a+b+ sqrt{ab} )}{a+b+ sqrt{ab} } = \ [/latex][latex]= frac{( sqrt{a} + sqrt{b})^{2}* ( sqrt{a} - sqrt{b} )(a+b+ sqrt{ab} )}{( sqrt{a} - sqrt{b} )( sqrt{a} + sqrt{b} )(a+b+ sqrt{ab})} = sqrt{a} + sqrt{b} [/latex]

(a+2√ab+b)/(a-b) * (a√a-b√b)/(a+b+√ab)==(√a+√b)²*(√*a-√b)(a+√ab+b)/(√a-√b)(√a+√b)*(a+√ab+b)=√a+√b