Вопрос:

Сократите дроби: 1) \(\frac{a^2-b^2}{a^2-2ab+b^2}\); 2) \(\frac{16-d^2}{d^2+8d+16}\); 3) \(\frac{x+6}{x^2+14x+48}\); 4) \(\frac{x^2-15x+50}{x-5}\); 5) \(\frac{2x^2-3x-5}{2x^2+x-1}\); 6) \(\frac{x^2+15x+50}{x+10}\); 7) \(\frac{y^2-9y+20}{y^2+y-30}\); 8) \(\frac{m^2-6m+9}{m^2-9}\); 9) \(\frac{x^2+5xy-6y^2}{x^2-4xy+3y^2}\); 10) \(\frac{x^2-2xy-3y^2}{x^2+3xy+2y^2}\); 11) \(\frac{3x^2+2x-1}{x^3+1}\); 12) \(\frac{x^2+x-6}{3x^2-4x-4}\).

Ответ:

  1. \(\frac{(a-b)(a+b)}{(a-b)^2}=\frac{a+b}{a-b}\), \(a
    e b\).
  2. \(\frac{(4-d)(4+d)}{(d+4)^2}=\frac{4-d}{d+4}\), \(d
    e-4\).
  3. \(\frac{x+6}{(x+6)(x+8)}=\frac1{x+8}\), \(x
    e-6,-8\).
  4. \(\frac{(x-5)(x-10)}{x-5}=x-10\), \(x
    e5\).
  5. \(\frac{(2x-5)(x+1)}{(2x-1)(x+1)}=\frac{2x-5}{2x-1}\), \(x
    e-1,\frac12\).
  6. \(\frac{(x+5)(x+10)}{x+10}=x+5\), \(x
    e-10\).
  7. \(\frac{(y-4)(y-5)}{(y+6)(y-5)}=\frac{y-4}{y+6}\), \(y
    e5,-6\).
  8. \(\frac{(m-3)^2}{(m-3)(m+3)}=\frac{m-3}{m+3}\), \(m
    e\pm3\).
  9. \(\frac{(x+6y)(x-y)}{(x-y)(x-3y)}=\frac{x+6y}{x-3y}\), \(x
    e y,3y\).
  10. \(\frac{(x-3y)(x+y)}{(x+y)(x+2y)}=\frac{x-3y}{x+2y}\), \(x
    e-y,-2y\).
  11. \(\frac{(3x-1)(x+1)}{(x+1)(x^2-x+1)}=\frac{3x-1}{x^2-x+1}\), \(x
    e-1\).
  12. \(\frac{(x+3)(x-2)}{(3x+2)(x-2)}=\frac{x+3}{3x+2}\), \(x
    e2,-\frac23\).
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