Упр.37.1 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (5m-n)/14m-(m-6n)/7m;
2) (a+b)/ab+(a-c)/ac;
3) (k+4)/k-(3k-4)/k^2 ;
4) (x-y)/x^3 -(y-x^2)/(x^2 y);
5) (2m-3n)/(m^2 n)+(7m-2n)/(mn^2 );
6) (c+d)/(cd^4 )-(c^2-8d)/(c^3 d^3 ).

1. $$\frac{5m-n}{14m}-\frac{m-6n}{7m}=\frac{5m-n-2(m-6n)}{14m}$$
   $$=\frac{5m-n-2m+12n}{14m}=\frac{3m+11n}{14m}$$

2. $$\frac{a+b}{ab}+\frac{a-c}{ac}=\frac{c(a+b)+b(a-c)}{abc}$$
   $$=\frac{ac+bc+ab-bc}{abc}=\frac{ac+ab}{abc}=\frac{a(c+b)}{abc}=\frac{b+c}{bc}$$

3. $$\frac{k+4}{k}-\frac{3k-4}{k^2}=\frac{k(k+4)-(3k-4)}{k^2}$$
   $$=\frac{k^2+4k-3k+4}{k^2}=\frac{k^2+k+4}{k^2}$$

4. $$\frac{x-y}{x^3}-\frac{y-x^2}{x^2y}=\frac{y(x-y)-x(y-x^2)}{x^3y}$$
   $$=\frac{xy-y^2-xy+x^3}{x^3y}=\frac{x^3-y^2}{x^3y}$$

5. $$\frac{2m-3n}{m^2n}+\frac{7m-2n}{mn^2}=\frac{n(2m-3n)+m(7m-2n)}{m^2n^2}$$
   $$=\frac{2mn-3n^2+7m^2-2mn}{m^2n^2}=\frac{7m^2-3n^2}{m^2n^2}$$

6. $$\frac{c+d}{cd^4}-\frac{c^2-8d}{c^3d^3}=\frac{c^2(c+d)-d(c^2-8d)}{c^3d^4}$$
   $$=\frac{c^3+c^2d-c^2d+8d^2}{c^3d^4}=\frac{c^3+8d^2}{c^3d^4}$$

Ответ

1) $$\frac{3m+11n}{14m}$$;
2) $$\frac{b+c}{bc}$$;
3) $$\frac{k^2+k+4}{k^2}$$;
4) $$\frac{x^3-y^2}{x^3y}$$;
5) $$\frac{7m^2-3n^2}{m^2n^2}$$;
6) $$\frac{c^3+8d^2}{c^3d^4}$$.