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Solve for x: (x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6 - Mathematics

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Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`

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Solution

Solution:

`(x-3)/(x-4)+(x-5)/(x-6)=10/3`

`[(x-3)(x-6)+(x-5)(x-4)]/((x-4)(x-6))=10/3`

`(x^2-9x+18+x^2-9x+20)/((x-4)(x-6))=10/3`

`(2x^2-18x+38)/((x-4)(x-6))=10/3`

`(2(x62-9x+19))/x=10/3(x^2-10x+24)`

`(x-9x+19)/1=5/3[x^2-10x+24]`

`3x^2-27x+57=5x^2-50x+120`

`2x^2-23x+63=0`

`x=7 or x=9/2`

 

Concept: Solutions of Quadratic Equations by Factorization
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