Ответы и объяснения

2013-09-15T09:01:09+00:00
1)  \frac{6x^2-3xz+10x-5z}{3x^2+5x} + \frac{z}{x} = \frac{3x(2x-z)+5(2x-z)}{x(3x+5)} + \frac{z}{x} =\frac{(3x+5)(2x-z)}{x(3x+5)} + \frac{z}{x} =
=\frac{2x-z}{x} + \frac{z}{x} =\frac{2x-z+z}{x}=\frac{2x}{x} =2

2) ( \frac{6a+1}{a^2-6a}+ \frac{6a-1}{a^2+6a} ) \frac{a^2-36}{a^2+1}=( \frac{6a+1}{a(a-6)}+ \frac{6a-1}{a(a+6)} ) \frac{(a-6)(a+6)}{a^2+1}=
=\frac{(6a+1)(a+6)+(6a-1)(a-6)}{a(a-6)(a+6)}* \frac{(a-6)(a+6)}{a^2+1}  =\frac{6a^2+37a+6+6a^2-37a+6}{a}* \frac{1}{a^2+1} =
=\frac{12(a^2+1)}{a}* \frac{1}{a^2+1}  = \frac{12}{a}

3) (p-q+ \frac{4q^2-p^2}{p+q} ):( \frac{p}{p^2-q^2} + \frac{2}{q-p}+ \frac{1}{p+q}  )=
=(p-q+ \frac{4q^2-p^2}{p+q} ):( \frac{p}{p^2-q^2} - \frac{2(p+q)}{(p-q)(p+q)}+ \frac{p-q}{(p-q)(p+q)}) =
=(p-q+ \frac{4q^2-p^2}{p+q} ):\frac{p-2p-2q+p-q}{p^2-q^2}=
=(p-q+ \frac{4q^2-p^2}{p+q} )\frac{q^2-p^2}{3q}= \frac{(q^2-p^2)(p^2-q^2+4q^2-p^2)}{3q(p+q)} = \frac{(q-p)(q+p)3q^2}{3q(p+q)}=
=q(q-p)

4)  \frac{4xy}{y^2-x^2} :( \frac{1}{y^2-x^2}+ \frac{1}{x^2+2xy+y^2})= \frac{4xy}{(y-x)(y+x)} :( \frac{1}{(y-x)(x+y)}+ \frac{1}{(x+y)^2})=
=\frac{4xy}{(y-x)(y+x)} :( \frac{x+y+y-x}{(y-x)(x+y)^2})=\frac{4xy}{(y-x)(y+x)}* \frac{(y-x)(x+y)^2}{2y}=2x(x+y)

5)( \frac{x^3+8}{x+2} +6x):(4-x^2)+ \frac{x-1}{x-2} =(x^2-2x+4+6x):(4-x^2)+ \frac{x-1}{x-2}=
=\frac{(x+2)^2}{(2-x)(2+x)} + \frac{x-1}{x-2}= \frac{x+2}{2-x}+ \frac{1-x}{2-x}=\frac{3}{2-x}

6)( \frac{1}{x-y} + \frac{3xy}{y^3-x^3} ):( \frac{x^2+y^2}{x^2-y^2} - \frac{x+y}{2x-2y} )=
=( \frac{1}{x-y} + \frac{3xy}{(y-x)(x^2+xy+y^2)} ):( \frac{x^2+y^2}{(x-y)(x+y)} - \frac{x+y}{2(x-y)} )=
=\frac{x^2+xy+y^2-3xy}{(x-y)(x^2+xy+y^2)} :\frac{2x^2+2y^2-x^2-2xy-y^2}{2(x-y)(x+y)}=\frac{(x-y)^2}{(x-y)(x^2+xy+y^2)} *\frac{2(x-y)(x+y)}{(x-y)^2}=
=\frac{2(x+y)}{x^2+xy+y^2}

7) \frac{a^3-15a^2+75a-125}{a^2-10a+25}+ \frac{25}{a+5} = \frac{(a-5)^3}{(a-5)^2}+ \frac{25}{a+5} =  a-5+ \frac{25}{a+5},a \neq 5
При а=1/2 a-5+ \frac{25}{a+5}= \frac{1}{2} -5+ \frac{25}{ \frac{1}{2}+5}=\frac{1}{2} -5+ \frac{50}{11}=\frac{11}{22} + \frac{100}{22}-5= \frac{111-110}{22}= \frac{1}{22}

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На доске:

а) 38/8 u 268/65
19*65 u 268*4
1235 > 1072
38/8 > 268/65

b) sqrt(5) u 38/17
25 u 38^2/17^2
25*17^2 u 38^2
35^2 < 38^2
sqrt(5) < 38/17

c) pi u sqrt(10,3)
pi^2 u 10,3
9,87 < 10,3
pi < sqrt(10,3)

А дальше я не поняла, в чем суть задания...
Ой! Сейчас всё остальное дорешаю))