Solve the following quadratic equations by factorization: 3/(x + 1) + 4/(x - 1) = 29/(4x - 1); x ≠ 1, (- 1), 1/4

Question

Solve the following quadratic equations by factorization:

\(\frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1};x\neq1,-1,\frac{1}{4}\)

Answer 1

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

\(\frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1};x\neq1,-1,\frac{1}{4}\)

⇒ (3x – 3 + 4x + 4)(4x – 1) = 29(x² – 1) 

⇒ (7x + 1)(4x – 1) = 29x² – 29 

⇒ 28x² – 3x – 1 = 29x² – 29 

⇒ x² + 3x – 28 = 0 

⇒ x² + 7x – 4x – 28 = 0 

⇒ x(x + 7) – 4(x + 7) = 0 

⇒ (x – 4)(x + 7) = 0 

⇒ x = 4, - 7