Алгебра: Спростіть вираз (2x+1/x-3+2x-1/x+3)*x2-9/10x2+15

Объяснение:2.1 2.2...

Спростіть вираз (2x+1/x-3+2x-1/x+3)*x2-9/10x2+15

Ответы

Amina1225 26.11.2021 22:10

Объяснение:

2.1 $( \frac{2x + 1}{x - 3} + \frac{2x - 1}{x + 3} ) \times \frac{x {}^{2} - 9}{10 x {}^{2} + 15} = \left(\frac{\left(2x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{\left(2x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\right)\times \left(\frac{x^{2}-9}{10x^{2}+15}\right) =\frac{\left(2x+1\right)\left(x+3\right)+\left(2x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\times \left(\frac{x^{2}-9}{10x^{2}+15}\right) =\frac{2x^{2}+6x+x+3+2x^{2}-6x-x+3}{\left(x-3\right)\left(x+3\right)}\times \left(\frac{x^{2}-9}{10x^{2}+15}\right) =\frac{6+4x^{2}}{\left(x-3\right)\left(x+3\right)}\times \left(\frac{x^{2}-9}{10x^{2}+15}\right) = \frac{\left(6+4x^{2}\right)\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)\left(10x^{2}+15\right)} =\frac{2\left(x-3\right)\left(x+3\right)\left(2x^{2}+3\right)}{5\left(x-3\right)\left(x+3\right)\left(2x^{2}+3\right)} =\frac{2}{5} = 0.4$

2.2

$(x - 3)(x + 3) - 4x \leqslant (x - 1) {}^{2} - 5 \\ x {}^{2} - 9 - 4x \leqslant (x - 1) {}^{2} - 5 \\ x {}^{2} - 9 - 4x \leqslant x {}^{2} - 2x + 1 - 5 \\ x {}^{2} - 9 - 4x \leqslant x {}^{2} - 2x - 4 \\ x {}^{2} - 9 - 4x - x {}^{2} \leqslant - 2x - 4 \\ - 9 - 4x \leqslant - 2x - 4 \\ - 9 - 4x + 2x \leqslant - 4 \\ - 9 - 2x \leqslant - 4 \\ - 2x \leqslant - 4 + 9 \\ - 2x \leqslant 5 \\ x \geqslant - \frac{5}{2} \\ x \geqslant - 2 \frac{1}{2}$