a) \(\frac{4x+3}{6x-4}+\frac{5x-9}{6x-4}\)
\(=\frac{4x+3+5x-9}{2\left(3x-2\right)}=\frac{9x-6}{2\left(3x-2\right)}\)
\(=\frac{3\left(3x-2\right)}{2\left(3x-2\right)}=\frac{3}{2}\)
b) \(\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{x^2-1}\)
\(=\frac{2\left(x+1\right)+3\left(x-1\right)-4x+2}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+1}{\left(x-1\right)\left(x+1\right)}=\frac{1}{x-1}\)
a) \(\frac{4x+3}{6x-4}+\frac{5x-9}{6x-4}\)
\(=\frac{4x+3+5x-9}{6x-4}\)
\(=\frac{9x-6}{6x-4}\)
\(=\frac{3.\left(3x-2\right)}{2.\left(3x-2\right)}\)
\(=\frac{3}{2}.\)
b) \(\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{x^2-1}\)
\(=\frac{2}{x-1}+\frac{3}{x+1}-\frac{4x-2}{\left(x-1\right).\left(x+1\right)}\)
\(=\frac{2.\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}+\frac{3.\left(x-1\right)}{\left(x-1\right).\left(x+1\right)}-\frac{4x-2}{\left(x-1\right).\left(x+1\right)}\)
\(=\frac{2x+2}{\left(x-1\right).\left(x+1\right)}+\frac{3x-3}{\left(x-1\right).\left(x+1\right)}+\frac{-\left(4x-2\right)}{\left(x-1\right).\left(x+1\right)}\)
\(=\frac{2x+2+3x-3-4x+2}{\left(x-1\right).\left(x+1\right)}\)
\(=\frac{x+1}{\left(x-1\right).\left(x+1\right)}\)
\(=\frac{1}{x-1}.\)
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