Задание 13 стр 105

Question

Выполните действия. 
$$a) \ \frac{x}{3(a-1)} -\frac{x}{4(a-1)} \quad b) \ \frac{a}{2(a+2)} - \frac{a}{a(a+2)} \quad c) \ \frac{3x}{2(x+y)} - \frac{2y}{3(x+y)}$$
$$d) \ \frac{b}{a(a-b)} -\frac{a}{b(a-b)} \quad e) \ \frac{x}{2x+2)} - \frac{x}{3x+3} \quad f) \ \frac{x}{5x-10} - \frac{x}{3x-6}$$

Gimli · Accepted Answer

a) $\frac{x}{3(a-1)}-\frac{x}{4(a-1)}=\frac{4 x-3 x}{3 \cdot 4 \cdot(a-1)}=\frac{x}{12(a-1)}=\frac{x}{12 a-12}$
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b) $\frac{a}{2(a+2)}-\frac{a}{a(a+2)}=\frac{a^2-2 a}{2 \cdot a(a+2)}=\frac{a(a-2)}{2 \cdot a(a+2)}=\frac{a-2}{2(a+2)}=\frac{a-2}{2 a+4}$
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c) $\frac{3 x}{2(x+y)}-\frac{2 y}{3(x+y)}=\frac{3 x \cdot 3-2 y \cdot 2}{2 \cdot 3 \cdot(x+y)}=\frac{9 x-4 y}{6(x+y)}=\frac{9 x-4 y}{6 x+6 y}$.
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d) $\frac{b}{a(a-b)}-\frac{a}{b(a-b)}=\frac{b^2-a^2}{a b(a-b)}=\frac{(b-a)(b+a)}{a b(a-b)}=-\frac{b+a}{a b}$.
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e) $\frac{x}{2 x+2}-\frac{x}{3 x+3}=\frac{x}{2(x+1)}-\frac{x}{3(x+1)}=\frac{3 x-2 x}{2 \cdot 3(x+1)}=\frac{x}{6(x+1)}=\frac{x}{6 x+6}$
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f) $\frac{x}{5 x-10}+\frac{x}{3 x-6}=\frac{x}{5(x-2)}+\frac{x}{3(x-2)}=\frac{3 x+5 x}{5 \cdot 3(x-2)}=\frac{8 x}{15(x-2)}=\frac{8 x}{25 x-30}$.

Задание 13 стр 105

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Задание 13 стр 105

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