Question

Solve for X :
one upon (x minus 1) into( x minus 2 )+ 1 upon x minus 2) into (x minus 3) is equal to 2 upon 3

Answer 1

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Answer 2

Answer:

$x=2\:Or\:x=0\:Or\:x=4$

Step-by-step explanation:

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

$\implies \frac{1}{(x-2)}[\frac{1}{(x-1)}+\frac{1}{(x-3)}]=\frac{2}{3}$

$\implies \frac{1}{(x-2)}[\frac{x-3+x-1}{(x-1)(x-3)}]=\frac{2}{3}$

$\implies \frac{1}{(x-2)}[\frac{2x-4}{(x-1)(x-3)}]-\frac{2}{3}=0$

$\implies \frac{2(x-2)}{(x-2)(x-1)(x-3)}-\frac{2}{3}=0$

$\implies \frac{6(x-2)-2(x-2)(x-1)(x-3)}{3(x-1)(x-2)(x-3)}=0$

$\implies 2(x-2)[3-(x-1)(x-3)]=0$

$\implies 2(x-2)=0\:Or\:3-(x-1)(x-3)=0$

$\implies x-2=0\:Or\:3-(x^{2}-4x+3)=0$

$\implies x=2\:Or\:3-x^{2}+4x-3=0$

$\implies x=2\:Or\:-x^{2}+4x=0$

$\implies x=2\:Or\:x(-x+4)=0$

$\implies x=2\:Or\:x=0\:Or\:-x+4=0$

$\implies x=2\:Or\:x=0\:Or\:x=4$

Therefore,

$x=2\:Or\:x=0\:Or\:x=4$

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