Find x in terms of a, b and c: a/(x-a)+b/(x-b)=(2c)/(x-c) - Mathematics

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Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`

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Solution

Consider the given equation:

`a/(x-a)+b/(x-b)=(2c)/(x-c)`

Taking the LCM and then cross multiplying, we get

`(a(x-b)+b(x-a))/((x-a)(x-b))=(2c)/(x-c)`

(xc)[a(xb)+b(xa)]=2c(xa)(xb)

(xc)[axab+bxab]=2c(x2bxax+ab)

ax22abx+bx2acx+2abcbcx=2cx22bcx2acx+2abc

ax2+bx22cx2=2abxacxbcx

(a+b2c)x2=x(2abacbc) 

(a+b2c)x2x(2abacbc)=0

x[(a+b2c)x(2abacbc)]=0

x=0 or (a+b2c)x(2abacbc)=0

x=0 or (a+b2c)x=(2abacbc)

`=>x = 0 `

Thus, the two roots of the given equation are x = 0 and `(2ab-ac-bc)/(a+b-2c)`

  Is there an error in this question or solution?
2015-2016 (March) Delhi Set 1

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