Question

Помогите решить примеры пж

Answer 1

$11)\frac{12xy}{25z}\div8xy^{2}=\frac{12xy}{25z}\div8\times xy^{2}=\frac{12xy}{25z}\times\frac{1}{8}\times\frac{xy^{2}}{1}=\frac{12xy\times1\times xy^{2}}{25z\times8}=\frac{3xy\times xy^{2}}{25z\times2}=\frac{3x^{2}y^{3}}{50z}$

$12)\frac{8b^{2}cd}{9a^{2}}\div\frac{7cd}{12a^{3}}=\frac{8b^{2}cd}{9a^{2}}\times\frac{12a^{3}}{7cd}=\frac{8b^{2}cd\times12a^{3}}{9a^{2}\times7cd}=\frac{8b^{2}\times4a}{3\times7}=\frac{32ab^{2}}{21}$

$13)\frac{a^{2}-25}{a^{2}-3a}\div\frac{a^{2}+5a}{a^{2}-9}=\frac{(a-5)(a+5)}{a(a-3)}\times\frac{a^{2}-9}{a^{2}+5a}=\frac{(a-5)(a+5)(a-3)(a+3)}{a(a-3)\times a(a+5)}=\frac{(a-5)(a+3)}{a\times a}=\frac{a^{2}+3a-5a-15}{a^{2}}=\frac{a^{2}-2a-15}{a^{2}}$

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

$15)\frac{a^{4}-b^{4}}{a^{3}-b^{3}}\div\frac{a^{2}+b^{2}}{a^{2}-b^{2}}=\frac{(a^{2}-b^{2})(a^{2}+b^{2})}{(a-b)(a^{2}+ab+b^{2})}\times\frac{a^{2}-b^{2}}{a^{2}+b^{2}}=\frac{(a^{2}-b^{2})(a^{2}+b^{2})(a^{2}-b^{2})}{(a-b)(a^{2}+ab+b^{2})(a^{2}+b^{2})}=\frac{(a-b)(a+b)(a^{2}-b^{2})}{(a-b)(a^{2}+ab+b^{2})}=\frac{(a+b)(a^{2}-b^{2})}{a^{2}+ab+b^{2}}=\frac{a^{3}-ab^{2}+a^{2}b-b^{3}}{a^{2}+ab+b^{2}}$