Question

ПОМОГИТЕ ПОЖАЛУЙСТА!!

Answer 1

1.

Дробь не имеет смысла, когда знаменатель $0$.

Тогда, $\implies x+3=0\implies x=-3$, а.

2.

$\вfrac{x-1}{x+1}=0\implies x-1=0\implies x=1$, в.

3.

а)

$\dfrac{a}{a+b}+\dfrac{b}{a+b}=\dfrac{a+b}{a+b}$, а не $\dfrac{a+b}{2(a+b)}$. Нет.

б)

$\dfrac{a}{a+b}+\dfrac{b}{a+b}=\dfrac{a+b}{a+b}=1$, а не $0$. Нет.

в)

$\dfrac{a}{a+b}+\dfrac{b}{a+b}=\dfrac{a+b}{a+b}=1$, да.

4.

а)

$\dfrac{12m^3}{6m^4}\div\dfrac{6m^3}{6m^3}\overset{\sqrt}{=}\dfrac{2}{m}$

б)

$\dfrac{3a^3b^4c}{24ab^6c}\div\dfrac{3ab^4c}{3ab^4c}=\dfrac{a^2}{8b^2}\ne\dfrac{1^ 3}{8b^2}$

в)

$\dfrac{(a-b)^3}{(b-a)^5}=\dfrac{(a-b)^3}{(-(a-b))^5}=\dfrac{(a-b)^3}{(-1)^5(a-b)^5}\div\dfrac{(a-b)^3}{(a-b)^3}=-\dfrac{1}{(a-b)^2}\overset{\sqrt}{=}\dfrac{-1}{(b-a)^2}$

5.

а)

$\dfrac{5a-b}{2a-b}+\dfrac{-3a}{2a-b}=\dfrac{5a-b+(-3a)}{2a-b}=\dfrac{2a-b}{2a-b}=1$

б)

$\dfrac{15m+3n}{5m+n}\div\dfrac{5m+n}{5m+n}-2=3-2=1$

6.

а)

$\dfrac{x^2-25y^2}{2x-10y}=\dfrac{(x-5y)(x+5y)}{2(x-5y)}\div\dfrac{x-5y}{x-5y}=\dfrac{x+5y}{2}$

б)

$\dfrac{a^2-2a+1}{a^2-1}=\dfrac{(a-1)^2}{(a-1)(a+1)}=\dfrac{a-1}{a+1}$

7.

$\dfrac{3}{x-5}-\dfrac{2}{x}+\dfrac{x-35}{x^2-25}=\dfrac{3}{x-5}\times\dfrac{x}{x}-\dfrac{2}{x}\times\dfrac{x-5}{x-5}+\dfrac{x-35}{(x-5)(x+5)}\\\\=\dfrac{3x-2(x-5)}{x(x-5)}+\dfrac{x-35}{(x-5)(x+5)}=\dfrac{x-10}{x(x-5)}\times\dfrac{x+5}{x+5}+\dfrac{x-35}{(x-5)(x+5)}\times\dfrac{x}{x}\\\\=\dfrac{(x-10)(x+5)+x(x-35)}{x(x-5)(x+5)}=\dfrac{2x^2-20x+50}{x(x-5)(x+5)}=\dfrac{2(x^2-10x+25)}{x(x-5)(x+5)}\\\\=\dfrac{2(x-5)^2}{x(x-5)(x+5)}\div\dfrac{x-5}{x-5}=\dfrac{2(x-5)}{x(x+5)}$

8.

$\dfrac{4}{a-b}+\dfrac{9}{a+b}-\dfrac{8a}{a^2-b^2}=\dfrac{4}{a-b}\times\dfrac{a+b}{a+b}+\dfrac{9}{a+b}\times\dfrac{a-b}{a-b}-\dfrac{8a}{(a-b)(a+b)}\\\\=\dfrac{4(a+b)+9(a-b)-8a}{(a-b)(a+b)}=\dfrac{4a+4b+9a-9b-8a}{(a-b)(a+b)}=\dfrac{5a-5b}{(a-b)(a+b)}\\\\=\dfrac{5(a-b)}{(a-b)(a+b)}\div\dfrac{a-b}{a-b}\overset{\sqrt}{=}\dfrac{5}{a+b}$

9.

$\dfrac{x^4-9x^2+54x-81}{x^3+27}=\dfrac{x^4-9x^2+54x-81}{(x+3)(x^2-3x+9)}$