+26367 Simplify.
\(\begin{array}{|rcll|} \hline && \dfrac{ \dfrac{x^2+2x-3}{x-4} } { \dfrac{2x^2+5x-3}{x^2-16} } \\\\ &=& \dfrac{(x^2+2x-3)}{(x-4)} \cdot \dfrac{(x^2-16)}{(2x^2+5x-3)} \quad & | \quad x^2-16 = (x-4)(x+4) \\\\ &=& \dfrac{(x^2+2x-3)}{(x-4)} \cdot \dfrac{(x-4)(x+4)}{(2x^2+5x-3)} \\\\ &=& \dfrac{(x^2+2x-3)}{1} \cdot \dfrac{(x+4)}{(2x^2+5x-3)} \\\\ &=& \dfrac{(x^2+2x-3)(x+4)}{(2x^2+5x-3)} \quad & | \quad x^2+2x-3 = (x-1)(x+3) \\\\ &=& \dfrac{(x-1)(x+3)(x+4)}{(2x^2+5x-3)} \quad & | \quad 2x^2+5x-3 = (2x-1)(x+3) \\\\ &=& \dfrac{(x-1)(x+3)(x+4)}{(2x-1)(x+3)} \\\\ &=& \dfrac{(x-1)(x+4)}{(2x-1)} \\\\ &\mathbf{=}& \mathbf{ \dfrac{x^2+3x-4}{(2x-1)} } \\ \hline \end{array}\)
