Problem 10.2. It is known that $\frac{a+b}{a-b}=3$. Find the value of the expression $\frac{a^{2}-b^{2}}{a^{2}+b^{2}}$.
Answer: 0.6.

Solution. Multiplying the equality $\frac{a+b}{a-b}=3$ by the denominator, we get $a+b=3a-3b$. Moving $a$ to the right and $3b$ to the left, we get $4b=2a$, from which $a=2b$. Substituting $a=2b$ into the second expression, we get

$$
\frac{4b^2-b^2}{4b^2+b^2}=0.6
$$