[tex] \frac{3x}{x {}^{2} - 3x - 10 } - \frac{6x}{x {}^{2} - 7x + 10} [/tex]

1 answer
Question:


[tex] \frac{3x}{x {}^{2} - 3x - 10 } - \frac{6x}{x {}^{2} - 7x + 10} [/tex]

Answers

[tex]\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)}[/tex]

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