Question

$frac{2a}{4a ^{2}-10ab } - frac{5b}{4a ^{2}-25b ^{2} } ; a=5. b= sqrt{3}$

Answer 1

$frac{2a}{4a ^{2}-10ab } - frac{5b}{4a ^{2}-25b ^{2} } =frac{2a}{2a(2a-5b) } - frac{5b}{(2a-5b)(2a+5b)} = \ frac{1}{(2a-5b) } - frac{5b}{(2a-5b)(2a+5b)} = frac{2a+5b}{(2a-5b)(2a+5b) } - frac{5b}{(2a-5b)(2a+5b)} = \ frac{2a+5b-5b}{(2a-5b)(2a+5b) }= frac{2a}{(2a-5b)(2a+5b) }= frac{2a}{4a ^{2}-25b ^{2} } \ \ a=5 \ b= sqrt{3} \ frac{2*5}{4*5 ^{2}-25( sqrt{3} )^{2} }= frac{10}{4*25-25*3} =frac{10}{100-75}= frac{10}{25} =0.4$