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| 1. |
1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)=1/6 |
| Answer» [{tex}1\\over(x-1)(x-2){/tex}+{tex}1\\over(x-2)(x-3){/tex}]+{tex}1\\over(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}(x-3)+(x-1)\\over(x-1)(x-2)(x-3){/tex}+{tex}1\\over (x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}2x-4\\over(x-1)(x-2)(x-3){/tex}+{tex}1\\over(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}2(x-2)\\over(x-1)(x-2)(x-3){/tex}+{tex}1\\over(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}2\\over(x-1)(x-3){/tex}+{tex}1\\over(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}2(x-4)+(x-1)\\over(x-1)(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}2x-8+x-1\\over(x-1)(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}3x-9\\over(x-1)(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}3(x-3)\\over(x-1)(x-3)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}3\\over(x-1)(x-4){/tex}={tex}1\\over6{/tex}=>{tex}(x-1)(x-4)=18{/tex}=>{tex}x\\ ^2-4x-x+4=18{/tex}=>{tex}x\\ ^2-5x-14=0{/tex}=>{tex}x\\ ^2-7x+2x-14=0{/tex}=>{tex}x(x-7)+2(x-7)=0{/tex}=>{tex}(x+2)(x-7)=0{/tex}=>{tex}either ,x+2=0 or, x-7=0{/tex}{tex}x=-2 or7{/tex} | |