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Semenov [28]
2 years ago
12

Subtract the rational expression 1/x^2-x-6 - x/x+2.

Mathematics
1 answer:
Aleksandr [31]2 years ago
4 0

Answer:

Step-by-step explanation:

x² - x -6 = x²  + 2x - 3x - 3*2

            =x(x + 2) - 3(x + 2)

            = (x + 2 )(x - 3)

\frac{1}{x^{2}-x-6}+\frac{x}{x+2}=\frac{1}{(x +2 )(x - 3)}-\frac{x}{x + 2}\\

                      = \frac{1}{(x+2)(x-3)}-\frac{x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x^{2}+3x}{(x+2)(x-3)}\\\\

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