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Question Number 152626 by mathdanisur last updated on 30/Aug/21

Solve for real numbers:  (1/(x-1)) + (2/(x-2)) + (3/(x-3)) + (4/(x-4)) = 2x^2 -5x-4

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}-\mathrm{1}}\:+\:\frac{\mathrm{2}}{\mathrm{x}-\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{x}-\mathrm{3}}\:+\:\frac{\mathrm{4}}{\mathrm{x}-\mathrm{4}}\:=\:\mathrm{2x}^{\mathrm{2}} -\mathrm{5x}-\mathrm{4} \\ $$

Answered by MJS_new last updated on 30/Aug/21

x=0  x=(5/2)  x=2±(√2)  x=3±(√2)

$${x}=\mathrm{0} \\ $$$${x}=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${x}=\mathrm{2}\pm\sqrt{\mathrm{2}} \\ $$$${x}=\mathrm{3}\pm\sqrt{\mathrm{2}} \\ $$

Commented by MJS_new last updated on 30/Aug/21

it′s very easy  (1) multiplicate with common denominator  (2) transform  (3) plain to see x=0  (4) substitute t=x−(5/2)  do something for yourself, not just copy our  answers!

$$\mathrm{it}'\mathrm{s}\:\mathrm{very}\:\mathrm{easy} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{multiplicate}\:\mathrm{with}\:\mathrm{common}\:\mathrm{denominator} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{transform} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{plain}\:\mathrm{to}\:\mathrm{see}\:{x}=\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{substitute}\:{t}={x}−\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\mathrm{do}\:\mathrm{something}\:\mathrm{for}\:\mathrm{yourself},\:\mathrm{not}\:\mathrm{just}\:\mathrm{copy}\:\mathrm{our} \\ $$$$\mathrm{answers}! \\ $$

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