Subjects algebra

Fraction Square E76A15

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1. The original problem involves simplifying an expression with a bracketed term from step 3, say $\left(\frac{a}{b} + c\right)$.\n2. As requested, we rewrite the bracketed term as a fraction with numerator 1, so it becomes $\frac{1}{\frac{b}{a} + \frac{1}{c}}$.\n3. Then, we square this entire fraction: $$\left(\frac{1}{\frac{b}{a} + \frac{1}{c}}\right)^2.$$\n4. To simplify, first find a common denominator inside the denominator: $$\frac{b}{a} + \frac{1}{c} = \frac{bc}{ac} + \frac{a}{ac} = \frac{bc + a}{ac}.$$\n5. Substitute back: $$\left(\frac{1}{\frac{bc + a}{ac}}\right)^2 = \left(\frac{1}{1} \cdot \frac{ac}{bc + a}\right)^2 = \left(\frac{ac}{bc + a}\right)^2.$$\n6. The final simplified expression is $$\boxed{\left(\frac{ac}{bc + a}\right)^2}.$$\nThis shows the bracketed term rewritten as a squared fraction with numerator 1 inside, then simplified fully.