Question

Помогите решить примеры пж

Answer 1

$11)frac{12xy}{25z}div8xy^{2}=frac{12xy}{25z}div8times xy^{2}=frac{12xy}{25z}timesfrac{1}{8}timesfrac{xy^{2}}{1}=frac{12xytimes1times xy^{2}}{25ztimes8}=frac{3xytimes xy^{2}}{25ztimes2}=frac{3x^{2}y^{3}}{50z}$

$12)frac{8b^{2}cd}{9a^{2}}divfrac{7cd}{12a^{3}}=frac{8b^{2}cd}{9a^{2}}timesfrac{12a^{3}}{7cd}=frac{8b^{2}cdtimes12a^{3}}{9a^{2}times7cd}=frac{8b^{2}times4a}{3times7}=frac{32ab^{2}}{21}$

$13)frac{a^{2}-25}{a^{2}-3a}divfrac{a^{2}+5a}{a^{2}-9}=frac{(a-5)(a+5)}{a(a-3)}timesfrac{a^{2}-9}{a^{2}+5a}=frac{(a-5)(a+5)(a-3)(a+3)}{a(a-3)times a(a+5)}=frac{(a-5)(a+3)}{atimes a}=frac{a^{2}+3a-5a-15}{a^{2}}=frac{a^{2}-2a-15}{a^{2}}$

$14)frac{x^{2}}{x^{2}+xy}divfrac{xy}{xy+y^{2}}=frac{x^{2}}{x(x+y)}timesfrac{xy+y^{2}}{xy}=frac{x^{2}times y(x+y)}{x(x+y)times xy}=frac{x^{2}times y(x+y)}{x^{2}times y(x+y)}=1$

$15)frac{a^{4}-b^{4}}{a^{3}-b^{3}}divfrac{a^{2}+b^{2}}{a^{2}-b^{2}}=frac{(a^{2}-b^{2})(a^{2}+b^{2})}{(a-b)(a^{2}+ab+b^{2})}timesfrac{a^{2}-b^{2}}{a^{2}+b^{2}}=frac{(a^{2}-b^{2})(a^{2}+b^{2})(a^{2}-b^{2})}{(a-b)(a^{2}+ab+b^{2})(a^{2}+b^{2})}=frac{(a-b)(a+b)(a^{2}-b^{2})}{(a-b)(a^{2}+ab+b^{2})}=frac{(a+b)(a^{2}-b^{2})}{a^{2}+ab+b^{2}}=frac{a^{3}-ab^{2}+a^{2}b-b^{3}}{a^{2}+ab+b^{2}}$