Solution: Let total articles be $ x $. $ 0.6x = 45 $. Divide: $ x = \frac{45}{0.6} = 75 $. \boxed{75}Question: If $\frac{a + b}{a - b} + \frac{a - b}{a + b} = 3$, find the value of $\frac{a^2 + b^2}{a^2 - b^2}$.

["SEO-Optimized Article: Solving the Algebraic Identity to Find $\frac{a^2 + b^2}{a^2 - b^2}$", "When faced with the equation\n$$\n\frac{a + b}{a - b} + \frac{a - b}{a + b} = 3,\n$$\nmany learners aim to determine the value of $\frac{a^2 + b^2}{a^2 - b^2}$. This problem combines rational expressions with algebraic identities—and offers a clear, structured solution anyone can follow.", "### Step 1: Let Total Variables Be $ x $ and Simplify", "Let:\n$$\nx = \frac{a + b}{a - b}\n\quad \Rightarrow \quad \frac{a - b}{a + b} = \frac{1}{x}\n$$\nSo the equation becomes:\n$$\nx + \frac{1}{x} = 3\n$$", "### Step 2: Multiply Both Sides by $ x $ to Eliminate the Denominator", "$$\nx^2 + 1 = 3x\n\Rightarrow x^2 - 3x + 1 = 0\n$$", "### Step 3: Target Expression Involves $ a^2 + b^2 $ and $ a^2 - b^2 $", "Recall:\n$$\na^2 + b^2 = \frac{(a + b)^2 + (a - b)^2}{2}, \quad a^2 - b^2 = (a + b)(a - b)\n$$\nSo:\n$$\n\frac{a^2 + b^2}{a^2 - b^2} = \frac{\frac{(a + b)^2 + (a - b)^2}{2}}{(a + b)(a - b)}\n$$\nLet $ u = a + b $, $ v = a - b $. Then:\n$$\n\frac{a^2 + b^2}{a^2 - b^2} = \frac{\frac{u^2 + v^2}{2}}{uv} = \frac{u^2 + v^2}{2uv}\n$$", "### Step 4: Use $ x = \frac{u}{v} $, So $ u = x v $", "Substitute $ u = x v $ into the expression:\n$$\n\frac{(xv)^2 + v^2}{2(xv)(v)} = \frac{x^2 v^2 + v^2}{2x v^2} = \frac{v^2(x^2 + 1)}{2x v^2} = \frac{x^2 + 1}{2x}\n$$", "### Step 5: Plug in $ x + \frac{1}{x} = 3 $ to Find $ x^2 + 1 $", "From earlier:\n$$\nx + \frac{1}{x} = 3\n\Rightarrow x^2 + 1 = 3x\n\Rightarrow \frac{x^2 + 1}{2x} = \frac{3x}{2x} = \frac{3}{2}\n$$", "### Final Answer:\n$$\n\frac{a^2 + b^2}{a^2 - b^2} = \boxed{\frac{3}{2}}\n$$", "---", "SEO Keywords: \nAlgebra challenge # Solve rational expressions # $\frac{a+b}{a-b} + \frac{a-b}{a+b} = 3$ # $x = \frac{a+b}{a-b}$ # Simplify expression # $x + \frac{1}{x} = 3$ # Algebraic identity # Mathematical problem solving # Olympiad preparation # High school math tip", "Meta Description:\nSolve for $\frac{a^2 + b^2}{a^2 - b^2}$ given $\frac{a+b}{a-b} + \frac{a-b}{a+b} = 3$. Follow step-by-step algebra to find the exact value: $\boxed{\frac{3}{2}}$."]