Question

Сократите дробь a3-b3/a4-b4 a5-b5/a3-b3 a3+a2b+ab2+b3/a4-b4 a3-8/a4-16

Answer 1

$1)\frac{a ^{3}-b ^{3} }{a ^{4}-b ^{4} }= \frac{(a-b)(a ^{2}+ab+b ^{2}) }{( a ^{2} -b ^{2})(a ^{2}+b ^{2}) }= \\ = \frac{a ^{2}+ab+b ^{2} }{(a+b)(a ^{2}+b ^{2}) }$
$2) \frac{a ^{5}-b ^{5} }{a ^{3}-b ^{3} }= \frac{(a-b)(a ^{4}+a ^{3}b+a ^{2}b ^{2} +ab ^{3}+b ^{4} )}{(a-b)(a ^{2}+ab+b ^{2} }= \frac{(a ^{4}+a ^{3}b+a ^{2}b ^{2} +ab ^{3}+b ^{4} ) }{(a ^{2}+ab+b ^{2} ) }$
$3) \frac{a ^{3}+a ^{2}b+ab ^{2}+b ^{3} }{a ^{4} -b ^{4} }= \frac{a ^{2}+a ^{2}b+ab ^{2}+b ^{2} }{(a-b)(a ^{3}+a ^{2}b+ab ^{2}+b ^{3} ) } }= \frac{1}{a-b}$
$4) \frac{a ^{3}-8 }{a ^{4}-16 }= \frac{(a-2)(a ^{2}+2a+4) }{(a-2)(a+2)(a ^{2}+4) }= = \frac{(a ^{2}+2a+4) }{(a+2)(a ^{2}+4) }$