Solve the following quadratic equations by factorization: 2/(x + 1) + 3/2(x - 2) = 23/5x; x ≠ 0, -1,2

Question

Solve the following quadratic equations by factorization:

\(\frac{2}{x + 1}+\frac{3}{2(x-2)}=\frac{23}{5x};x\neq0,-1,2\)

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

\(\frac{2}{x + 1}+\frac{3}{2(x-2)}=\frac{23}{5x};x\neq0,-1,2\)

⇒ 5x(4x – 8 + 3x + 3) = 46(x + 1)(x – 2) 

⇒ 35x² – 25x = 46x² – 92 – 46x 

⇒ 11x² - 19x - 92 = 0 

⇒ 11x² - 44x + 23x – 92 = 0 

⇒ 11x(x – 4) + 23(x – 4) = 0 

⇒ (11x + 23)(x – 4) = 0 

⇒ x = 4, - 23/11