Упражнении дли повторении курса 7-9 классов — Тождественные преобразования — 710 — стр. 192

\(\left(\frac{7(m-2)}{m^3-8}-\frac{m+2}{m^2+2m+4}\right) \cdot \frac{2m^2+4m+8}{m-3}\)

\(\frac{7(m-2)-(m+2)(m-2)}{(m-2)\left(m^2+2m+4\right)} \cdot \frac{2\left(m^2+2m+4\right)}{m-3}\)

\(\frac{(7-m-2) \cdot 2}{m-3}=\frac{10-2m}{m-3}\).

\(\frac{a+5}{a^2-9}:\left(\frac{a+2}{a^2-3a+9}-\frac{2(a+8)}{a^3+27}\right)\)

\(\frac{a+5}{a^2-9}: \frac{(a+2)(a+3)-2a-16}{(a+3)\left(a^2-3a+9\right)}\)

\(\frac{a+5}{(a-3)(a+3)} \cdot \frac{(a+3)\left(a^2-3a+9\right)}{a^2+2a+3a+6-2a-16}\)

\(\frac{a+5}{a-3} \cdot \frac{a^2-3a+9}{a^2+3a-10}\)

\(\frac{a+5}{a-3} \cdot \frac{a^2-3a+9}{(a-2)(a+5)}\)

\(\frac{a^2-3a+9}{(a-2)(a-3)}=\frac{a^2-3a+9}{a^2-5a+6}\)

\(a^2+3a-10=0, \ a_{1,2}=\frac{-3\pm\sqrt{9+40}}{2}, \ a_1=2, \ a_2=-5\).

\(\left(\frac{x+2}{3x}-\frac{2}{x-2}-\frac{x-14}{3x^2-6x}\right): \frac{x+2}{6x} \cdot \frac{1}{x-5}\)

\(\frac{(x+2)(x-2)-2 \cdot 3x-(x-14)}{3x(x-2)}: \frac{x+2}{6x} \cdot \frac{1}{x-5}\)

\(\frac{x^2-4-6x-x+14}{3x(x-2)} \cdot \frac{6x}{x+2} \cdot \frac{1}{x-5}\)

\(\frac{2x^2-14x+20}{(x-2)(x+2)(x-5)}\)

\(\frac{2(x-5)(x-2)}{(x-2)(x+2)(x-5)}=\frac{2}{x+2}\)

\(2x^2-14x+20=0, \ x_{1,2}=\frac{14\pm\sqrt{196-160}}{4}, \ x_1=5, \ x_2=2\).

\(\left(\frac{4x}{9-x^2}-\frac{x-3}{9+3x}\right) \cdot \frac{18}{x+3}-\frac{2x}{3-x}\)

\(\frac{12x-(x-3)(3-x)}{3(3-x)(3+x)} \cdot \frac{18}{x+3}-\frac{2x}{3-x}\)

\(\frac{12x+(x-3)^2}{(3-x)(3+x)} \cdot \frac{6}{x+3}-\frac{2x}{3-x}\)

\(\frac{\left(12x+x^2-6x+9\right) \cdot 6}{(3-x)(x+3)^2}-\frac{2x}{3-x}\)

\(\frac{6(x+3)^2-2x(x+3)^2}{(3-x)(x+3)^2}=\frac{2(3-x)}{3-x}=2\).