\(\dfrac{2x}{2x+10}-\dfrac{x-1}{2x^2+10}\)
\(=\dfrac{x}{x+5}-\dfrac{x-1}{2x^2+10}\)
\(=\dfrac{x\left(2x^2+10\right)-\left(x-1\right)\left(x+5\right)}{\left(x+5\right)\left(2x^2+10\right)}\)
\(=\dfrac{2x^3+10x-\left(x^2+5x-x-5\right)}{\left(x+5\right)\left(2x^2+10\right)}\)
\(=\dfrac{2x^3+10x-x^2-4x+5}{\left(x+5\right)\left(2x^2+10\right)}\)
\(=\dfrac{2x^3-x^2+6x+5}{\left(x+5\right)\left(2x^2+10\right)}\)
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