# Solve the Following Quadratic Equation by Factorization: 3/(x+1)-1/2 = 2/(3x-1), x≠-1,1/3

By BYJU'S Exam Prep

Updated on: October 17th, 2023

x = 1, and 3 are the zeros of the equation.

In order to solve the given quadratic equation, we will use factorization method. And then to solve the quadratic equation by factorization, we need to bring all the terms to one side of the equation and then factorize it.

To do so, we will first eliminate fractions and then solve entire equation on one side adn equate it to 0 in order to get the desired result. Let us see the detailed solution below.

## Solve the Following Quadratic Equation by Factorization: 3/(x+1)-1/2 = 2/(3x-1), x≠-1,1/3

Solution:

Given quadratic equation = 3/(x+1)-1/2 = 2/(3x-1)

Multiplying both sides of the equation by the denominators to eliminate fractions:

[3×2 – (x+1)]/(x+1)2 = 2/(3x-1)

[6- x-1]/(2x+2) = 2/(3x-1)

Expanding and simplifying the equation:

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

15x-5-3x2+x = 4x + 4

On solving, we get:

-3x2+12x -9 = 0

On further solving, we get

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

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

Hence, x = 1, 3