Упр.487 ГДЗ Муравин 7 класс (Алгебра)

1) n/(n-1) при n = -1/3;
2) (a^2 + 1)/(a — 4) при a = 3,5;
3) (ab — 1)/(a + 1)(b + 1,6) при a = -1,5, b = 3,2;
4) ((2c + 3x)c)/(x — c) — x при c = 1,2, x = 1,3.

1. При $$n=-\frac13$$:

   $$ \frac{n}{n-1}=\frac{-\frac13}{-\frac13-1}=\frac{-\frac13}{-\frac43}=\frac13\cdot\frac34=\frac14. $$

2. При $$a=3{,}5$$:

   $$ \frac{a^2+1}{a-4}=\frac{3{,}5^2+1}{3{,}5-4}=\frac{12{,}25+1}{-0{,}5}=\frac{13{,}25}{-0{,}5}=-26{,}5. $$

3. При $$a=-1{,}5$$, $$b=3{,}2$$:

   $$ \frac{ab-1}{(a+1)(b+1{,}6)}= \frac{-1{,}5\cdot 3{,}2-1}{(-1{,}5+1)(3{,}2+1{,}6)}= \frac{-4{,}8-1}{-0{,}5\cdot 4{,}8}= \frac{-5{,}8}{-2{,}4}=\frac{29}{12}=2\frac{5}{12}. $$

4. При $$c=1{,}2$$, $$x=1{,}3$$:

   $$ \frac{(2c+3x)c}{x-c}-x= \frac{(2\cdot 1{,}2+3\cdot 1{,}3)\cdot 1{,}2}{1{,}3-1{,}2}-1{,}3 $$

   $$ =\frac{(2{,}4+3{,}9)\cdot 1{,}2}{0{,}1}-1{,}3 =\frac{6{,}3\cdot 1{,}2}{0{,}1}-1{,}3 =75{,}6-1{,}3=74{,}3. $$

Ответ

1) $$\frac14$$; 2) $$-26{,}5$$; 3) $$2\frac{5}{12}$$; 4) $$74{,}3$$.