a) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)
\(=\dfrac{3x+5-5+15x}{4x^3y}\)
\(=\dfrac{18x}{4x^3y}\)
\(=\dfrac{9}{2x^2y}\)
b) \(\dfrac{2}{x-2}+\dfrac{4}{x+2}+\dfrac{-6+5x}{4-x^2}\)
\(=\dfrac{2}{x-2}+\dfrac{4}{x+2}+\dfrac{6-5x}{x^2-4}\)
\(=\dfrac{2\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}+\dfrac{4\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\dfrac{6-5x}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{2\left(x+2\right)+4\left(x-2\right)+6-5x}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{2x+4+4x-8+6-5x}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x+2}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{1}{x-2}\)
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