Question

СРОЧНОООООО ПОЖААААЛУУСТА ХЕЛП!!!​

Answer 1

1)

$(\frac{a}{a+1} +1):(1-\frac{3a^{2}}{1-a^{2}} )=(\frac{a}{a+1} +\frac{a+1}{a+1} ):(\frac{1-a^{2}}{1-a^{2}}-\frac{3a^{2}}{1-a^{2}})=\frac{2a+1}{a+1} :\frac{1-4a^{2}}{(1-a)(1+a)} =\\\\\frac{2a+1}{a+1} :\frac{(1-2a)(1+2a)}{(1-a)(1+a)} =\frac{(2a+1)(1-a)(1+a)}{(a+1)(1-2a)(1+2a)} =\frac{1-a}{1-2a}$

2)

$(\frac{2m+1}{2m-1} -\frac{2m-1}{2m+1}):\frac{4m}{10m-5} =(\frac{(2m+1)(2m+1)}{(2m-1)(2m+1)} -\frac{(2m-1)(2m-1)}{(2m-1)(2m+1)} ):\frac{4m}{5(2m-1)} =\\\\(\frac{4m^{2}+2m+2m+1}{4m^{2}-1} -\frac{4m^{2}-2m-2m+1}{4m^{2}-1} ):\frac{4m}{5(2m-1)} =\frac{4m^{2}+4m+1-4m^{2}+4m-1}{4m^{2}-1} :\frac{4m}{5(2m-1)} =\\\\\frac{8m}{(2m-1)(2m+1)} :\frac{4m}{5(2m-1)} =\frac{8m*5(2m-1)}{(2m-1)(2m+1)*4m} =\frac{2*5}{2m+1} =\frac{10}{2m+1}$

3)

$(\frac{a+1}{2a-2} +\frac{6}{2a^{2}-2} -\frac{a+3}{2a+2} )*\frac{4a^{2}-4}{3} =(\frac{a+1}{2(a-1)} +\frac{6}{2(a-1)(a+1)} -\frac{a+3}{2(a+1)})*\frac{4(a-1)(a+1)}{3} =\\\\(\frac{(a+1)(a+1)}{2(a-1)(a+1)} +\frac{6}{2(a-1)(a+1)} -\frac{(a+3)(a-1)}{2(a-1)(a+1)})* \frac{4(a-1)(a+1)}{3} =(\frac{a^{2}+2a+1}{2(a-1)(a+1)} +\frac{6}{2(a-1)(a+1)}-\\\\\frac{a^{2}+2a-3}{2(a-1)(a+1)} )*\frac{4(a-1)(a+1)}{3}=\frac{10}{2(a-1)(a+1)} *\frac{4(a-1)(a+1)}{3} =\frac{20}{3}$

4)

$(\frac{5a}{a+x} +\frac{5x}{a-x} +\frac{10ax}{a^{2}-x^{2}} )(\frac{a}{a+x} +\frac{x}{a-x} -\frac{2ax}{a^{2}-x^{2}} )=\frac{5a(a-x)+5x(a+x)+10ax}{(a+x)(a-x)} *\frac{a(a-x)+x(a+x)-2ax}{(a+x)(a-x)} =\\\\\frac{5a^{2}-5ax+5ax+5x^{2}+10ax}{(a+x)(a-x)} *\frac{a^{2}-ax+ax+x^{2}-2ax}{(a+x)(a-x)} =\frac{5(a^{2}+2ax+x^{2})}{(a+x)(a-x)} *\frac{a^{2}-2ax+x^{2}}{(a+x)(a-x)} =\\\\\frac{5(a+x)(a+x)}{(a+x)(a-x)} *\frac{(a-x)(a-x)}{(a+x)(a-x)} =5$