Question

помогите пожалуйста решить 573 и 574

Answer 1

573
1)$( frac{a}{a+1} + frac{a+1}{a+1} ):( frac{1- a^{2} }{1- a^{2} } - frac{3a ^{2} }{1- a^{2} } )= frac{2a+1}{a+1} * frac{(1+a)(1-a)}{(1-2a)(1+2a) } = frac{1-a}{1-2a}$
2)$( frac{(2m+1)(2m+1)}{4m^{2} -1} - frac{(2m-1)(2m-1)}{4m ^{2}-1 } )* frac{10m-5}{4m} = frac{(2m+1) ^{2} -(2m-1) ^{2} }{(2m+1)(2m-1)} * frac{5(2m-1)}{4m} =$$frac{4m ^{2}+1+4m-4m ^{2}-1+4m }{2m+1} * frac{5}{4m} = frac{4m}{2m+1} * frac{5}{4m}= frac{5}{2m+1}$
3)($frac{a(x+a)}{(x-a)(x+a)} + frac{a(x-a)}{(x-a)(x+a)} )* frac{(x+a) ^{2} }{2 a^{2} } = frac{a(x+a)+a(x-a)}{(x-a)(x+a)} * frac{(x+a) ^{2} }{2a ^{2} } = frac{2ax}{x-a} * frac{x+a}{2a ^{2} }$=$frac{ x^{2} +ax}{ax- a^{2} }$
4)$( frac{x ^{3} }{xy ^{2} } + frac{ y^{3} }{xy ^{2} } ):( frac{ x^{2} }{xy ^{2} } - frac{xy}{xy ^{2} } + frac{y ^{2} }{xy ^{2} } )= frac{x ^{3}+y ^{3} }{xy ^{2} } * frac{xy ^{2} }{ x^{2} -xy+y ^{2} } = frac{x ^{3} +x^{3} }{ x^{2} -xy+y ^{2} }$