Question

Выражение: 1) 2/3-a+a^2-4/a^2-9*a+3/a-2 2)ab/a^2-b^2: ab/a+b-b/a^2-b^2 п.с. / дробная черта, a^2 а во 2 степени, * умножение, : обычное деление !

Answer 1

1) $\frac{2}{3-a}+\frac{a^{2}-4}{a^{2}-9}\cdot\frac{a+3}{a-2}=\frac{a}{a-3}$

1) $\frac{a^{2}-4}{a^{2}-9}\cdot\frac{a+3}{a-2}=\frac{(a-2)(a+2)}{(a-3)(a+3)}\cdot\frac{a+3}{a-2}=\frac{a+2}{a-3}$

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

2) $\frac{ab}{a^{2}-b^{2}}:\frac{ab}{a+b}-\frac{b}{a^{2}-b^{2}}=\frac{a}{a^{2}-b^{2}}$

1) $\frac{ab}{a^{2}-b^{2}}:\frac{ab}{a+b}=\frac{ab}{a^{2}-b^{2}}\cdot\frac{a+b}{ab}=\frac{ab}{(a+b)(a-b)}\cdot\frac{a+b}{ab}=\frac{1}{a-b}$

2) $\frac{1}{a-b}-\frac{b}{a^{2}-b^{2}}=\frac{1}{a-b}-\frac{b}{(a-b)(a+b)}=\frac{a+b-b}{(a-b)(a+b)}= \frac{a}{a^{2}-b^{2}}$