Question

Нужно сократить дроби: ^ - степень. * - умножить. \ - дробная черта. 1) 36a^3b^2c-36a^3b^3\48ab^5-48ab^3c^2 2) (m-n)^2\m^2-n^2 3) 6pq-18p\(q-3)^2 4) c^2-18c+81\c-9 5) 5-2m\4m^2-20m+25 6) b^2-49\49-14b+b^2 7) 4n^2-4nm+m^2\4n^2-m^2 8) a^2-ab-b-c^2\b^2-a^2+2ac-c^2 9) x^2-yz+xz-y^2\x^2+yz-xz-y^2 10) 8^11-8^10-8^9\4^15-4^14-4^13 11) 87^3+43^3\87^2-87*43+43^2

Answer 1

1) 36a^3b^2c-36a^3b^3\48ab^5-48ab^3c^2 =                                                = 36a^3b^2(c - b) / 48ab^3(b^2-c^2) = 3a^2(c-b) /4(b-c)(b+c) =
 = -3a^2/4b(b+c)

2) (m-n)^2\m^2-n^2 = (m-n)^2 / (m-n)(m+n) = (m-n)/(m+n)

3) 6pq-18p\(q-3)^2 = 6p(q - 3)/(q - 3)^2 = 6p/(q-3)

4) c^2-18c+81\c-9 = (c-9)^2 / (c-9) = c - 9

5) 5-2m\4m^2-20m+25 = (5 - 2m)/(5-2m)^2 = 1/(5-2m)

6) b^2-49\49-14b+b^2 = (b-7)(b+7)/(b-7)^2= (b+7)/(b-7)

7) 4n^2-4nm+m^2\4n^2-m^2 = (2n-m)^2 / (2n-m)(2n+m) =(2n-m)/(2n+m)

8) a^2-ab-bс-c^2\b^2-a^2+2ac-c^2 = [(a^2-c^2) - b(a+c)] / [b^2 - (a-c)^2] =
   = [(a-c)(a+c) - b(a+c)] / [(b-(a-c)(b+(a-c)] = [(a+c)(a-c-b)]/ [-(a-c-b)(a+b-c)]=
= -(a+c)/(a+b-c)

9) x^2-yz+xz-y^2\x^2+yz-xz-y^2 =                                                                     =  [(x^2-y^2) - z(x-y)] / [(x^2-y^2) - z(x-y)]=1

10) 8^11-8^10-8^9\4^15-4^14-4^13 = 8^4(1-1^6-1^5) / 4^12(1^3-1^2-1) =
 = 8^4 (1-1-1)/4^12(1-1-1) = 8^4/4^12

11) 87^3+43^3\87^2-87*43+43^2 =
   = (87+43)(87^2-87*43+43^2)/(87^2-87*43+43^2) =(87+43) = 130