\(\frac{11x+13}{3x-3}+\frac{15x+17}{4-4x}\)
\(=\frac{11x+13}{3\left(x-1\right)}+\frac{15x+17}{4\left(1-x\right)}\)
\(=\frac{11x+13}{3\left(x-1\right)}+\frac{-\left(15x+17\right)}{4\left(x-1\right)}\)
\(=\frac{\left(11x+13\right).4}{3\left(x-1\right).4}+\frac{-\left(15x+17\right).3}{4\left(x-1\right).3}\)
\(=\frac{44x+52}{12\left(x-1\right)}+\frac{-45x-51}{12\left(x-1\right)}\)
\(=\frac{44x+52-45x-51}{12\left(x-1\right)}=\frac{1-x}{12\left(x-1\right)}=\frac{-\left(x-1\right)}{12\left(x-1\right)}=-\frac{1}{12}\)
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