Сократите рациональные дроби. Блок 1: 1) 2x/(3x); 2) 15x/(20y); 3) 6x/(12y); 4) 4ab/(12bc); 5) 2xy/(5xy²); 6) 10xy/(15ya); 7) 2ay³/(4a²y); 8) 24ac²/(6ac); 9) 63x²y³/(42x⁶y); 10) 6x²y/(3y). Блок 2: 1) a(b+2)/(b(b+2)); 2) ax(a+b)/(x(a+b)); 3) 2(a−b)/(4(a−b)); 4) 6(a−2b)/(a−2b); 5) a²(a+x)/(a(a+x)); 6) (x−b)/(b−x); 7) 3(a−3b)/(6(3b−a)); 8) −4(2a−6)/(6−2a); 9) 3a²(a−4)/(a⁴(a−4)); 10) −21(4a−3b)/(−49(3b−4a)). Блок 3: 1) (3a+12b)/(6ab); 2) (2a−4)/(3(a−2)); 3) (a−3b)/(a²−3ab); 4) 10a/(15a−20b); 5) (5xy+10x)/(6y+12); 6) (3a²+15ab)/(a+5b); 7) (ab−2a)/(5b−10); 8) (3a+12)/(ac+4c); 9) ab(y+3)/(a²by+3a²b); 10) a⁴(b−2c)/(a²b−2a²c).

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Фото задания

Сократите рациональные дроби. Блок 1: 1) 2x/(3x); 2) 15x/(20y); 3) 6x/(12y); 4) 4ab/(12bc); 5) 2xy/(5xy²); 6) 10xy/(15ya); 7) 2ay³/(4a²y); 8) 24ac²/(6ac); 9) 63x²y³/(42x⁶y); 10) 6x²y/(3y). Блок 2: 1) a(b+2)/(b(b+2)); 2) ax(a+b)/(x(a+b)); 3) 2(a−b)/(4(a−b)); 4) 6(a−2b)/(a−2b); 5) a²(a+x)/(a(a+x)); 6) (x−b)/(b−x); 7) 3(a−3b)/(6(3b−a)); 8) −4(2a−6)/(6−2a); 9) 3a²(a−4)/(a⁴(a−4)); 10) −21(4a−3b)/(−49(3b−4a)). Блок 3: 1) (3a+12b)/(6ab); 2) (2a−4)/(3(a−2)); 3) (a−3b)/(a²−3ab); 4) 10a/(15a−20b); 5) (5xy+10x)/(6y+12); 6) (3a²+15ab)/(a+5b); 7) (ab−2a)/(5b−10); 8) (3a+12)/(ac+4c); 9) ab(y+3)/(a²by+3a²b); 10) a⁴(b−2c)/(a²b−2a²c).

Accepted Answer

Сокращаем числитель и знаменатель на общий множитель.

Блок 1:

\(\frac{2x}{3x}=\frac{2}{3}\).
\(\frac{15x}{20y}=\frac{3x}{4y}\).
\(\frac{6x}{12y}=\frac{x}{2y}\).
\(\frac{4ab}{12bc}=\frac{a}{3c}\).
\(\frac{2xy}{5xy^2}=\frac{2}{5y}\).
\(\frac{10xy}{15ya}=\frac{2x}{3a}\).
\(\frac{2ay^3}{4a^2y}=\frac{y^2}{2a}\).
\(\frac{24ac^2}{6ac}=4c\).
\(\frac{63x^2y^3}{42x^6y}=\frac{3y^2}{2x^4}\).
\(\frac{6x^2y}{3y}=2x^2\).

Блок 2:

\(\frac{a(b+2)}{b(b+2)}=\frac{a}{b}\).
\(\frac{ax(a+b)}{x(a+b)}=a\).
\(\frac{2(a-b)}{4(a-b)}=\frac{1}{2}\).
\(\frac{6(a-2b)}{a-2b}=6\).
\(\frac{a^2(a+x)}{a(a+x)}=a\).
\(\frac{x-b}{b-x}=\frac{-(b-x)}{b-x}=-1\).
\(\frac{3(a-3b)}{6(3b-a)}=\frac{3(a-3b)}{-6(a-3b)}=-\frac{1}{2}\).
\(\frac{-4(2a-6)}{6-2a}=\frac{-8(a-3)}{-2(a-3)}=4\).
\(\frac{3a^2(a-4)}{a^4(a-4)}=\frac{3}{a^2}\).
\(\frac{-21(4a-3b)}{-49(3b-4a)}=-\frac{3}{7}\).

Блок 3:

\(\frac{3a+12b}{6ab}=\frac{3(a+4b)}{6ab}=\frac{a+4b}{2ab}\).
\(\frac{2a-4}{3(a-2)}=\frac{2(a-2)}{3(a-2)}=\frac{2}{3}\).
\(\frac{a-3b}{a^2-3ab}=\frac{a-3b}{a(a-3b)}=\frac{1}{a}\).
\(\frac{10a}{15a-20b}=\frac{10a}{5(3a-4b)}=\frac{2a}{3a-4b}\).
\(\frac{5xy+10x}{6y+12}=\frac{5x(y+2)}{6(y+2)}=\frac{5x}{6}\).
\(\frac{3a^2+15ab}{a+5b}=\frac{3a(a+5b)}{a+5b}=3a\).
\(\frac{ab-2a}{5b-10}=\frac{a(b-2)}{5(b-2)}=\frac{a}{5}\).
\(\frac{3a+12}{ac+4c}=\frac{3(a+4)}{c(a+4)}=\frac{3}{c}\).
\(\frac{ab(y+3)}{a^2by+3a^2b}=\frac{ab(y+3)}{a^2b(y+3)}=\frac{1}{a}\).
\(\frac{a^4(b-2c)}{a^2b-2a^2c}=\frac{a^4(b-2c)}{a^2(b-2c)}=a^2\).

Ответ: Блок 1: \(\frac23;\ \frac{3x}{4y};\ \frac{x}{2y};\ \frac{a}{3c};\ \frac{2}{5y};\ \frac{2x}{3a};\ \frac{y^2}{2a};\ 4c;\ \frac{3y^2}{2x^4};\ 2x^2\). Блок 2: \(\frac ab;\ a;\ \frac12;\ 6;\ a;\ -1;\ -\frac12;\ 4;\ \frac3{a^2};\ -\frac37\). Блок 3: \(\frac{a+4b}{2ab};\ \frac23;\ \frac1a;\ \frac{2a}{3a-4b};\ \frac{5x}{6};\ 3a;\ \frac a5;\ \frac3c;\ \frac1a;\ a^2\).