ГДЗ з алгебри 8 клас Істер, вправа №4.6

1) $\frac{10x+3(x-4)}{15} = \frac{13x-12}{15}$

2) $\frac{4m-2n-2(m-n)}{10} = \frac{2m}{10} = \frac{m}{5}$

3) $\frac{3(a+2)-2(3-7a)}{12a} = \frac{17a}{12a}$

4) $\frac{x(2-3y)-y(5-3x)}{xy} = \frac{2x-5y}{xy}$

5) $\frac{3y(x+7)-x(3y+4)}{15xy} = \frac{21y-4x}{15xy}$

6) $\frac{3b(4a+b)+2a(a-6b)}{6ab} = \frac{3b^2+2a^2}{6ab}$

1) $\frac{2x}{3}+\frac{x-4}{5} = \frac{5 \cdot 2x + 3(x-4)}{15} = \frac{10x+3x-12}{15} = \frac{13x-12}{15}$

2) $\frac{4m-2n}{10}-\frac{m-n}{5} = \frac{4m-2n-2(m-n)}{10} = \frac{4m-2n-2m+2n}{10} = \frac{2m}{10} = \frac{m}{5}$

3) $\frac{a+2}{4a}-\frac{3-7a}{6a} = \frac{3(a+2)-2(3-7a)}{12a} = \frac{3a+6-6+14a}{12a} = \frac{17a}{12a}$

4) $\frac{2-3y}{y}-\frac{5-3x}{x} = \frac{x(2-3y)-y(5-3x)}{xy} = \frac{2x-3xy-5y+3xy}{xy} = \frac{2x-5y}{xy}$

5) $\frac{x+7}{5x}-\frac{3y+4}{15y} = \frac{3y(x+7)-x(3y+4)}{15xy} = \frac{3xy+21y-3xy-4x}{15xy} = \frac{21y-4x}{15xy}$

6) $\frac{4a+b}{2a}+\frac{a-6b}{3b} = \frac{3b(4a+b)+2a(a-6b)}{6ab} = \frac{12ab+3b^2+2a^2-12ab}{6ab} = \frac{3b^2+2a^2}{6ab}$