Question

Упростите выражение:

1) 5/х^2+5х + х+15/25-х^2=
2)1/х+3 + 9/х^3+27=
3)2/х + 12/х^2-6х - 1-х/х-6=​

Answer 1

1)

$\frac{5}{ {x}^{2} + 5x } + \frac{x + 15}{25 - {x}^{2} } = \frac{5}{x(x + 5)} + \frac{x + 15}{ {5}^{2} - {x}^{2} } = \frac{5}{x(x + 5)} + \frac{x + 15}{(5 - x)(5 + x)} = \frac{5 \times (5 - x)}{x(x + 5) \times (5 - x)} + \frac{(x + 15) \times x}{(5 - x)(5 + x) \times x} = \frac{25 - 5x}{x(5 - x)(5 + x)} + \frac{ {x}^{2} + 15x }{x(5 - x)(5 + x)} = \frac{25 - 5x + {x}^{2} + 15x }{x(5 - x)(5 + x)} = \frac{25 + 10x + {x}^{2} }{x(5 - x)(5 + x)} = \frac{ {(5 + x)}^{2} }{x(5 - x)(5 + x)} = \frac{5 + x}{x(5 - x)} = \frac{5 + x}{5x - {x}^{2} }$

2)

$\frac{1}{x + 3} + \frac{9}{ {x}^{3} + 27 } = \frac{1}{x + 3} + \frac{9}{ {x}^{3} + {3}^{3} } = \frac{1}{x + 3} + \frac{9}{(x + 3)( {x}^{2} - 3x + 9)} = \frac{1 \times ( {x}^{2} - 3x + 9) }{(x + 3) \times ( {x}^{2} - 3x + 9) } + \frac{9}{(x + 3)( {x}^{2} - 3x + 9) } = \frac{ {x}^{2} - 3x + 9 + 9 }{(x + 3)( {x}^{2} - 3x + 9)} = \frac{ {x}^{2} - 3x + 18 }{ {x}^{3} + 27}$

3)

$\frac{2}{x} + \frac{12}{ {x}^{2} - 6x } - \frac{1 - x}{x - 6} = \frac{2}{x} + \frac{12}{x(x - 6)} - \frac{1 - x}{x - 6} = \frac{2 \times (x - 6)}{x \times (x - 6)} + \frac{12}{x(x - 6)} - \frac{(1 - x) \times x}{(x - 6) \times x} = \frac{2x - 12}{ x(x - 6)} + \frac{12}{ x(x - 6)} - \frac{x - {x}^{2} }{ x(x - 6) } = \frac{2x - 12 + 12 - x + {x}^{2} }{ x(x - 6) } = \frac{ {x}^{2} + x }{ x(x - 6) } = \frac{x(x + 1)}{x(x - 6)} = \frac{x + 1}{x - 6}$