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電子課本網(wǎng) 第64頁

第64頁

信息發(fā)布者:
$?解:方程兩邊同時乘以2(x+3),得$
$2(x-2)=x+3$
$ 2x-4=x+3$
$ 2x-x=3+4$
$ x=7$
$檢驗:當(dāng)x=7時,2(x+3)≠0,$
$故x=7是原分式方程的解。$
$? 解:方程兩邊同時乘以x(x-2),得$
$ x=3(x-2)$
$ x=3x-6$
$-2x=-6$
$ x=3$
$檢驗:當(dāng)x=3時,x(x-2)≠0,$
$故x=3是原分式方程的解。$
$解:方程兩邊同時乘以(x-1)(x+2),得$
$2x(x+2)+2(x-1)=2(x-1)(x+2)$
$ 2{x}^{2}+6x-2=2{x}^{2}+2x-4$
$ 6x-2x=-4+2$
$ 4x=-2$
$ x=-\frac 1 2$
$檢驗:當(dāng)x=-\frac 1 2時,(x-1)(x+2)≠0,$
$故x=-\frac 1 2是原分式方程的解。$
$解:方程兩邊同時乘以(x-3)(x-1),得$
$(2x-3)(x-3)-(x-3)(x-1)=(x+2)(x-1)$
$(2{x}^{2}-9x+9)-({x}^{2}-4x+3)={x}^{2}+x-2$
${x}^{2}-5x+6={x}^{2}+x-2$
$-5x-x=-2-6$
$-6x=-8$
$x=\frac 4 3$
$檢驗:當(dāng)x=\frac 4 3時,(x-3)(x-1)≠0,$
$故x=\frac 4 3是原分式方程的解$
$解:方程兩邊同時乘以?(x-1)(x-2)(x-4)(x-5),?得$
$?(x-4)(x-5)=(x-1)(x-2)?$
$? {x}^2-9x+20={x}^2-3x+2?$
$? -9x+3x=2-20?$
$? -6x=-18?$
$? x=3?$
$檢驗:當(dāng)?x=3?時,?(x-1)(x-2)(x-4)(x-5)\neq 0,?$
$故是原分式方程的解。$
$解:原分式方程可化為,$
$(1+{\frac {1} {x-1}})-(1+{\frac {1} {x-2}})=(1+{\frac {1} {x-4}})-(1+{\frac {1} {x-5}})$
${\frac {1} {x-1}}-{\frac {1} {x-2}}={\frac {1} {x-4}}-{\frac {1} {x-5}}$
${\frac {(x-2)-(x-1)} {(x-1)(x-2)}}={\frac {(x-5)-(x-4)} {(x-4)(x-5)}}$
${\frac {-1} {(x-1)(x-2)}={\frac {-1} {(x-4)(x-5)}}}$
${\frac {1} {(x-1)(x-2)}}={\frac {1} {(x-4)(x-5)}}$
$由(1)知,原分式方程的解為x=3$