Chapter 10 - Radical Expressions and Equations - 10-3 Operations With Radical Expressions - Practice and Problem-Solving Exercises - Page 630: 40

The answer is: $x=2(3-2\sqrt2)$.

Given: $(\sqrt2-1)/(\sqrt2+1)=x/2$ By cross multiplication we get, $(\sqrt2-1)*2=x*(\sqrt2+1)$ $2(\sqrt2-1)/(\sqrt2+1)=x$ $x=2(\sqrt2-1)/(\sqrt2+1)*(\sqrt2-1)/(\sqrt2-1)$ Multiplying and dividing by $(\sqrt2-1)$: $x=2(\sqrt2-1)^{2}/(\sqrt2^{2}-1^{2})$ $x=2(2+1-2*\sqrt2*1)/(2-1)$ $x=2(3-2\sqrt2)/(1)$ $x=2(3-2\sqrt2)$.