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Solve the equation 3/(x+1)-1/2=2/(3x-1);x≠-1 ,x≠1/3 - CBSE Class 10 - Mathematics

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Question

Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`

Solution

`3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3, `

This can be rewritten as:

`3/(x+1)-2/(3x-1)=1/2`

`(3(3x-1)-2(x+1))/((x+1)(3x-1))=1/2`

`(7x-5)/(3x^2+2x-1)=1/2`

On cross multiplying, we get:

2(7x-5)=3x2+2x-1

14x-10=3x2+2x-1

3x2-12x+9=0

3x2-9x-3x+9=0

3x(x-3)-3(x-3)=0

(3x-3)(x-3)=0

3(x-1)(x-3)=0

(x-1)(x-3)=0

x=1,3

Thus, the solution of the given equation is 1 or 3.

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Solution Solve the equation 3/(x+1)-1/2=2/(3x-1);x≠-1 ,x≠1/3 Concept: Solutions of Quadratic Equations by Factorization.
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