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avatar+389 

Simplify.

Hev123  May 30, 2018
 #1
avatar+20710 
+1

Simplify.

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

 

 

laugh

heureka  Jun 1, 2018

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