Question

1). упростить2). упростить 3) найти значение выраж.

Answer 1

1) $\frac{8k+ k^{2}+ 16 }{ 15k^{2} + 3k } : \frac{16-k^{2} }{25 k^{2}- 1 }=\frac{(k+4)^2}{3k(5k+1)} \cdot \frac{(5k-1)(5k+1)}{(4-k)(4+k)}=\frac{(k+4)(5k-1)}{3k(4-k)}$

2)  $\frac{ \frac{1}{a} + \frac{1}{b+c} }{ \frac{1}{a}- \frac{1}{b+c} } * ( 1+ \frac{b^{2}+ c^{2}-a^{2} }{2bc} )= \frac{\frac{b+c+a}{a(b+c)}}{\frac{b+c-a}{a(b+c)}}\cdot \frac{2bc+b^2+c^2-a^2}{2bc}= \\ =\frac{b+c+a}{b+c-a}\cdot \frac{(b+c)^2-a^2}{2bc}=\frac{b+c+a}{b+c-a}\cdot \frac{(b+c-a)(b+c+a)}{2bc}= \\ =\frac{(a+b+c)^2}{2bc}$

3)  $(\frac{x+1}{x-1}-\frac{x-1}{x+1}) : (\frac{x^{2}+1}{x^{2}-}-\frac{x^{2}-1}{x^{2}+1})x=-3\frac {3}{4} \\ \frac{(x+1)^2-(x-1)^2}{(x-1)(x+1)} : \frac{(x^{2}+1)^2-(x^{2}-1)^2}{(x^{2}-1)(x^{2}+1)}x=-3\frac {3}{4} \\ \frac{(x+1-x+1)(x+1+x-1)}{(x-1)(x+1)} : \frac{(x^{2}+1-x^{2}+1)(x^{2}+1+x^{2}-1)}{(x^{2}-1)(x^{2}+1)}x=-3\frac {3}{4} \\ \frac{4x}{(x-1)(x+1)} : \frac{4x^{2}}{(x^{2}-1)(x^{2}+1)}x=-3\frac {3}{4} \\ \frac{4x}{(x-1)(x+1)}\cdot \frac{(x^{2}-1)(x^{2}+1)}{4x^{2}}x=-3\frac {3}{4}$
$x^2+1=-3\frac {3}{4} \\ x^2=-4\frac {3}{4}$
решения нет