21 tháng 11 2023 lúc 11:57
1. ĐKXĐ: \(x\ne5\)
\(\dfrac{3x+1}{x-5}+\dfrac{-2x-6}{x-5}\)
\(=\dfrac{3x+1-2x-6}{x-5}\)
\(=\dfrac{x-5}{x-5}\)
\(=1\)
2. ĐKXĐ: \(x\ne\pm1\)
\(\dfrac{x+1}{2x-2}-\dfrac{x^2+3}{2x^2-2}\)
\(=\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x^2+3}{2\left(x^2-1\right)}\)
\(=\dfrac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}-\dfrac{x^2+3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{2x-2}{\left(2x-2\right)\left(x+1\right)}\)
\(=\dfrac{1}{x+1}\)
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