Question

Не знаю как скорачивать 1) 2m^2-72n^2/(4m+24n)^2?

2) a^3-8/ab-a-2b+2?

3)a^3+2a^2b+ab^2/a^3-ab^2?

Answer 1

$1)\frac{2m^{2}-72n^{2}}{(4m+24n)^{2}}=\frac{2(m^{2}-36n^{2})}{(4m+24n)(4m+24n)}=\frac{2(m-6n)(m+6n)}{4*4*(m+6n)(m+6n)}=\frac{m-6n}{8(m+6n)}}$

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

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