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Title: Math 118 -- Combining Algebraic Fractions Post by: Centennial College on Mar 7, 2022 Question 1:
\(\frac{x+6}{2}+x=\frac{4x+3}{6}\) LCD: 6, thus, multiply both sides by 6: \(6\left(\frac{x+6}{2}+x\right)\ =6\left(\frac{4x+3}{6}\right)\) \(\frac{6\left(x+6\right)}{2}+6x=\frac{6\left(4x+3\right)}{6}\) Simplify: \(3\left(x+6\right)+6x=4x+3\) \(3x+6x-4x=3-18\) \(5x=-15\) \(x=-\frac{15}{5}=-3\) Question 2: \(\frac{x}{10}-\frac{x-6}{5}-\frac{x-8}{15}=0\) LCD: 30, thus, multiply both sides by 30: \(30\left(\frac{x}{10}\right)-30\left(\frac{x-6}{5}\right)-30\left(\frac{x-8}{15}\right)=0\) \(3x-6\left(x-6\right)-2\left(x-8\right)=0\) Expand: \(3x-6x+36-2x+16=0\) Gather like-terms: \(3x-6x-2x=-36-16\) \(-5x=-52\) \(x=\frac{-52}{-5}=\frac{52}{5}\) Question 3: \(\frac{9n+12}{15}-\frac{4n-7}{5}-\frac{4}{10}=1\) LCD: 30, thus, multiply both sides by 30: \(30\left(\frac{9n+12}{15}\right)-30\left(\frac{4n-7}{5}\right)-30\left(\frac{4}{10}\right)=1\) \(2\left(9n+12\right)-6\left(4n-7\right)-3\left(4\right)=1\) \(18n+24-24n+42-12=0\) \(18n-24n=12-42-24\) \(-6n=-54\) \(n=\frac{-54}{-6}=9\) |