Question

Помогите упростить примеры и решить уравнение. Буду благодарен.

Answer 1

1.
$\frac{{x}^{2} + x - 6 }{ {x}^{2} + 3x - 10} = \frac{(x + 3)(x - 2)}{(x + 5)(x - 2)} = \frac{x + 3}{x + 5}$
2.
$= ( \frac{2a + 3}{ {(a + 2)}^{2} } - \frac{x + 1}{a(a + 2)} ) \times \frac{a(4 - {a}^{2}) }{ {a}^{2} - 2 } = \frac{a(2a + 3) - (a + 1)(a + 2)}{a {(a + 2)}^{2} } \times \frac{a(4 - {a}^{2} )}{ {a}^{2} - 2} = \frac{2 {a}^{2} + 3a - {a}^{2} - a - 2a - 2}{a {(a + 2)}^{2} } \times \frac{a(2 - a)(2 + a)}{ {a}^{2} - 2} = \frac{ {a}^{2} - 2 }{(a + 2)} \times \frac{2 - a}{ {a}^{2} - 2} = \frac{2 - a}{a + 2}$
3.
$\frac{ \sqrt{x} }{ \sqrt{x} + 3} - \frac{x}{x - 9} = \frac{ \sqrt{x} }{ \sqrt{x} + 3 } - \frac{x}{( \sqrt{x} - 3)( \sqrt{x} + 3) } = \frac{ \sqrt{x}( \sqrt{x} - 3) - x}{( \sqrt{x} + 3)( \sqrt{x} - 3)} = \frac{ - 3 \sqrt{x} }{( \sqrt{x} + 3)( \sqrt{x} - 3)}$
4.
$= \frac{7 - 5\sqrt{2} - (7 + 5\sqrt{2} ) }{(7 + 5 \sqrt{2})(7 - 5 \sqrt{2} )} = -\frac{ - 10 \sqrt{2} }{ - 1} = 10 \sqrt{2}$
5.
$( \frac{9}{x - 4} - x - 4) \div \frac{ {x}^{2} - 10x + 25 }{4 - x} = \frac{9 - (x + 4)(x - 4)}{x - 4} \times \frac{4 - x}{ {(x - 5)}^{2} } = \frac{9 - {x}^{2} + 16}{ {(x - 5)}^{2} } = \frac{25 - {x}^{2} }{ {(x - 5)}^{2} } = \frac{(5 - x)(5 + x)}{ {(x - 5)}^{2} } = \frac{5 + x}{x - 5}$