Question

Докажите тождество (№5) заранее !

Answer 1

Объяснение:

5.

1) ((3b/(b-2))-6b/(b²-4b+4)= ((3b/(b-2))-6b/(b-2)²)=(3b*(b-2)-6b)/(b-2)²=

=(3b²-6b-6b)/(b-2)²=(3b²-12b)/(b-2)²=3b*(b-4)/(b-2)².

2) (3b*(b-4)/(b-2)²):(b-4)/(b²-4)=3b*(b-4)*(b-2)*(b+2)/((b-2)²*(b-4)=

=3b*(b+2)/(b-2).

3) 3b*(b+2)/(b-2)-(2b²+8b)/((b-2)=(3b²+6b-2b²-8b)/(b-2)=

=(b²-2b)/(b-2)=b*(b-2)/(b-2)=b.

Answer 2

$( \frac{3b}{b - 2} - \frac{6b}{ {b}^{2} - 4b + 4 } ) \div \frac{b - 4}{ {b}^{2} - 4} - \frac{2b {}^{2} + 8b }{b - 2} = ( \frac{3b}{b - 2} - \frac{6b}{ (b - 2) {}^{2} } ) \times \frac{b {}^{2} - 4}{ {b} - 4} - \frac{2b {}^{2} + 8b }{b - 2} = \\ = \frac{3b(b - 2) - 6b}{ {(b - 2)}^{2} } \times \frac{b {}^{2} - 4}{ {b} - 4} - \frac{2b {}^{2} + 8b }{b - 2} = \frac{(3 {b {}^{2} - 6b - 6b)(b - 2)(b + 2)} }{(b - 2) {}^{2} (b - 4)} - \frac{2b {}^{2} + 8b }{b - 2} = \\ = \frac{(3b { }^{2} - 12b) (b + 2)}{(b - 2)(b - 4)} - \frac{2b {}^{2} + 8b }{b - 2} = \frac{3b(b - 4)(b + 2)}{(b - 2)(b - 4)} - \frac{2b {}^{2} + 8b }{b - 2} = \frac{3b(b + 2)}{b - 2} - \frac{2b {}^{2} + 8b }{b - 2} = \\ = \frac{3 {b }^{2} + 6b - 2b {}^{2} - 8b }{b - 2} = \frac{b {}^{2} - 2b }{b - 2} = \frac{b(b - 2)}{b - 2} = b \\ \\ b = b$