<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%7D%7Bx%20%7B%7D%5E%7B2%7D%20-%203x%20-%2010%20%7D%20%20-%20%20%5Cfrac%7B6x%7D%

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3 years ago

7Bx%20%7B%7D%5E%7B2%7D%20%20-%207x%20%2B%2010%7D%20" id="TexFormula1" title=" \frac{3x}{x {}^{2} - 3x - 10 } - \frac{6x}{x {}^{2} - 7x + 10} " alt=" \frac{3x}{x {}^{2} - 3x - 10 } - \frac{6x}{x {}^{2} - 7x + 10} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Alex Ar [27]3 years ago

4 0

$\bf \cfrac{3x}{x^2-3x-10}-\cfrac{6x}{x^2-7x+10}\implies \cfrac{3x}{(x-5)(x+2)}-\cfrac{6x}{(x-5)(x-2)}
\\\\\\
\textit{our LCD is clearly then }(x-5)(x+2)(x-2)
\\\\\\
\cfrac{(x-2)3x~~-~~[(x+2)6x]}{(x-5)(x+2)(x-2)}\implies \cfrac{3x^2-6x~~-~~[6x^2+12x]}{(x-5)(x+2)(x-2)}
\\\\\\
\cfrac{3x^2-6x-6x^2-12x}{(x-5)(x+2)(x-2)}\implies \cfrac{-3x^2-18x}{(x-5)(x+2)(x-2)}$

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