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Reil [10]
3 years ago
11

0%5Cfrac%7B4%7D%7Bx%20%2B%203%7D%20%20" id="TexFormula1" title="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " alt="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " align="absmiddle" class="latex-formula">

Mathematics
1 answer:
malfutka [58]3 years ago
7 0

\frac{3 +  \frac{x - 3}{9 -  {x}^{2} } }{3 -\frac{4}{x + 3} }  \\  =  \frac{ \frac{3(9 -  {x}^{2} ) + x - 3}{9 -  {x}^{2} } }{ \frac{3(x + 3) - 4}{x + 3} }  \\  =  \frac{27 - 3 {x}^{2}  + x - 3}{9 -  {x}^{2} }  \times  \frac{x + 3}{3x + 12 - 4}  \\  =  \frac{ - 3 {x}^{2} + x + 24 }{ - (x - 3)(x + 3)}  \times  \frac{x + 3}{3x + 8}  \\  =   \frac{ - (3x + 8)(x - 3)}{ - (x - 3)}  \times  \frac{1}{3x + 8}  \\  =   \frac{ - (x - 3)}{ - (x - 3)}  \\  = 1

Hope this helps. - M
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