Question

Помогите сделать алгебру.

Answer 1

1)
$\frac{3}{3a-1}*\frac{(3a-1)(3a+1)}{5a-2}=\frac{9a+3}{5a-2}$
$\frac{7-a-9a-3}{5a-2}=\frac{4-10a}{5a-2}=\frac{-2(5-a}{5-a}=-2$

2)
$\frac{3}{x-1}-\frac{2}{x+1}=\frac{3x+3-2x+2}{(x-1)(x+1)}=\frac{x+5}{x^{2}-1}$
$\frac{x+5}{x^{2}-1}*\frac{-(x^{2}-1)}{x(x+5)}=-\frac{1}{x}$

3)
$\frac{m}{m+2}*\frac{(m+2)(m-2)}{m}=m-2$
$\frac{10-3m-6+5m}{m+2}=\frac{4+2m}{m+2}=\frac{2(2+m)}{m+2}=2$
2+m-2=m

4) 
$\frac{a}{1}-\frac{a^{2}-2}{a-1}=\frac{a^{2}-2a+1}{a+2}=\frac{a-2}{a-1}$
$\frac{a-2}{a-1}*\frac{a^{2}-2a+1}{a+2}=\frac{a-2}{a-1}*\frac{(a-1)(a-1)}{a+2}=\frac{(a-2)(a-1)}{a+2}$
D=4-4=0
a=2:2=1

5)
1)$\frac{3m}{m+5}-\frac{8m}{(m+5)(m+5)}=\frac{3m^{2}+15m-8m}{(m+5)(m+5)}=\frac{3m^{2}+7m}{(m+5)(m+5)}$
D=100-4*25=0
m=(-10)/2=-5
2)$\frac{m(3m+7)}{(m+5)(m+5)}*\frac{(m-5)(m+5)}{3m+7}=\frac{m^{2}-5m}{m+5}$
3)$\frac{m^{2}-5m+5m-25}{m+5}=\frac{m^{2}-25}{m+5}=\frac{(m-5)(m+5)}{m+5}=m-5$