Math, asked by GouthamGS9717, 9 months ago

Solve the following quadratic equations by factorization:
(3/x+1)-1/2=(2/3x-1),x≠-1,1/3

Answers

Answered by ashishks1912
3

The values of x in the given quadratic equation is 1 and 3

Step-by-step explanation:

Given equation is \frac{3}{x-1}-\frac{1}{2}=\frac{2}{3x-1} and x\neq 1,\frac{1}{3}

To solve the given equation by Factorization method :

  • \frac{3}{x-1}-\frac{1}{2}=\frac{2}{3x-1}
  • \frac{3(2)-1(x+1)}{(x+1)(2)}=\frac{2}{3x-1}
  • \frac{6-x-1}{x(2)+x(2)}=\frac{2}{3x-1}  
  • \frac{5-x}{2x+2}=\frac{2}{3x-1}
  • (5-x)(3x-1)=2(2x+2)
  • 5(3x)+5(-1)-x(3x)-x(-1)=2(2x)+2(2)
  • 15x-5-3x^2+x=4x+4
  • 16x-3x^2-5=4x+4
  • 16x-3x^2-5-(4x-4)=4x+4-(4x+4)
  • 16x-3x^2-5-4x-4=0
  • 12x-3x^2-9=0
  • -3x^2+12x-9=0
  • -3(x^2-4x+3)=0

Dividing by 3 on both sides

  • \frac{-3(x^2-4x+3)}{3}=\frac{0}{3}
  • x^2-4x+3=0
  • (x-1)(x-3)=0
  • x-1=0 or x-3=0
  • x=1 or x=3
  • Therefore x=1,3

The values of x in the given quadratic equation is 1 and 3

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