第85页 - 亮点给力提优课时作业本八年级数学江苏版

D

C

$-\frac {2}{m²-1}$

1

$=\frac {m+n}{m+n}+\frac {\mathrm {m^2}}{n^2-\mathrm {m^2}}$

$=1+\frac {\mathrm {m^2}}{n^2-\mathrm {m^2}}$

$=\frac {n^2}{n^2-\mathrm {m^2}}$

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

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

$=\frac {a-1}{a+1}$

解：∵$\frac {A}{x-1} - \frac {B}{2-x} = \frac {A}{x-1} + \frac {B}{x-2} = \frac {A(x-2)+B(x-1)}{(x-1)(x-2)}= \frac {(A+B)x-2A-B}{(x-1)(x-2)}$，

且$\frac {A}{x-1}-\frac {B}{2-x}=\frac {2x-6}{(x-1)(x-2)}$

∴$A+B=2$，$2A+B=6$，解得$A=4$，$B=-2$

则$A$，$B$的值分别是$4$，$-2$

M=N

解：由题意，得$b-a=1$，$c-a=2$，$c-b=1$

原式$=\frac {a²+b²+c²-bc-ac-ab}{abc}=\frac { (b-a)²+(c-a)²+(c-b)² }{2abc}$

又$abc=6072$，∴原式$=\frac {1+4+1}{2×6072}=\frac {1}{2024}$