Упр.468 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) (1/2 a^3 b^2-3/4 ab^4 ) 4/3 a^3 b;
2) (2/3 a^2 b^4+1/2 a^3 b) 3/2 ab^3;
3) (1 4/7 a^3 x^3-2 3/4 a^2 x^3-11ax^4 )(-2 6/11 ax^6 );
4) (-2 4/9 b^6 y+2 1/5 b^3 y^2-11by^5 )(-2 1/22 b^4 y^5 ).
Выполнить действия:
1) 2/(x^2-9)+1/(x+3);
2) (5+p^2)/(p^2-36)-p/(6+p);
3) 2x/(x-4)-(5x-2)/(x^2-16).

1. $$\left(\frac12 a^3b^2-\frac34 ab^4\right)\frac43 a^3b$$

   $$\frac12\cdot\frac43\,a^6b^3-\frac34\cdot\frac43\,a^4b^5=\frac23a^6b^3-ab^5.$$

2. $$\left(\frac23 a^2b^4+\frac12 a^3b\right)\frac32 ab^3$$

   $$\frac23\cdot\frac32\,a^3b^7+\frac12\cdot\frac32\,a^4b^4=a^3b^7+\frac34a^4b^4.$$

3. $$\left(1\frac47 a^3x^3-2\frac34 a^2x^3-11ax^4\right)\left(-2\frac6{11}ax^6\right)$$

   $$\left(\frac{11}{7}a^3x^3-\frac{11}{4}a^2x^3-11ax^4\right)\left(-\frac{28}{11}ax^6\right)$$

   $$-\frac{28}{7}a^4x^9+\frac{28}{4}a^3x^9+28a^2x^{10}=-4a^4x^9+7a^3x^9+28a^2x^{10}.$$

4. $$\left(-2\frac49 b^6y+2\frac15 b^3y^2-11by^5\right)\left(-2\frac1{22}b^4y^5\right)$$

   $$\left(-\frac{22}{9}b^6y+\frac{11}{5}b^3y^2-11by^5\right)\left(-\frac{45}{22}b^4y^5\right)$$

   $$5b^{10}y^6-\frac{9}{2}b^7y^7+\frac{45}{2}b^5y^{10}.$$

5. $$\frac{2}{x^2-9}+\frac{1}{x+3}$$

   $$x^2-9=(x-3)(x+3)$$

   $$\frac{2}{(x-3)(x+3)}+\frac{1}{x+3}=\frac{2+x-3}{x^2-9}=\frac{x-1}{x^2-9}.$$

6. $$\frac{5+p^2}{p^2-36}-\frac{p}{6+p}$$

   $$p^2-36=(p-6)(p+6)$$

   $$\frac{5+p^2}{(p-6)(p+6)}-\frac{p}{p+6}=\frac{5+p^2-p(p-6)}{p^2-36}$$

   $$\frac{5+p^2-p^2+6p}{p^2-36}=\frac{5+6p}{p^2-36}.$$

7. $$\frac{2x}{x-4}-\frac{5x-2}{x^2-16}$$

   $$x^2-16=(x-4)(x+4)$$

   $$\frac{2x(x+4)}{x^2-16}-\frac{5x-2}{x^2-16}=\frac{2x(x+4)-5x+2}{x^2-16}$$

   $$\frac{2x^2+8x-5x+2}{x^2-16}=\frac{2x^2+3x+2}{x^2-16}.$$

Ответ

1. $$\frac23a^6b^3-ab^5$$
2. $$a^3b^7+\frac34a^4b^4$$
3. $$-4a^4x^9+7a^3x^9+28a^2x^{10}$$
4. $$5b^{10}y^6-\frac92b^7y^7+\frac{45}{2}b^5y^{10}$$
5. $$\frac{x-1}{x^2-9}$$
6. $$\frac{5+6p}{p^2-36}$$
7. $$\frac{2x^2+3x+2}{x^2-16}$$