Question

4/x²-9 - 2/x²+3x
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Answer 1

Пошаговое объяснение:

$\frac{4}{ {x}^{2} - 9} - \frac{2}{ {x}^{2} -+3x } = \\ = \frac{4}{( {x} - 3)(x + 3)} - \frac{2}{x( {x}+3) } = \\ = \frac{4x}{x( {x} - 3)(x + 3)} - \frac{2(x -3)}{x( {x}- 3) (x + 3)} = \\ = \frac{4x - 2(x -3)}{x( {x}- 3) (x + 3)} = \\ = \frac{4x - 2x + 2 \cdot3}{x( {x}- 3) (x + 3)} = \\ = \frac{ 2x +6}{x( {x}- 3) (x + 3)} = \frac{ 2 \cancel{(x +3)}}{x\cancel{(x + 3)} (x -3)} = \\ = \frac{2}{x(x - 3)} = \frac{2}{ {x}^{2} - 3x }$

Answer 2

$\displaystyle \frac{4}{ {x}^{2} - 9 } - \frac{2}{ {x}^{2} + 3x } = \frac{ 4}{(x - 3)(x + 3)} - \frac{2}{x(x + 3)} = \frac{4x - 2(x - 3)}{x(x - 3)(x + 3)} = \frac{4x - 2x + 6}{x(x - 3)(x + 3)} = \frac{2x + 6}{x(x - 3)(x + 3)} = \frac{2(x + 3)}{x(x - 3)(x + 3)} = \frac{2}{x(x - 3)} = \frac{2}{x^2-3x} .$