Solve the following quadratic equations by factorization: (x - 3)/(x + 3) - (x + 3)/(x - 3) = 48/7, ≠ 3, x ≠ - 3

Question

Solve the following quadratic equations by factorization:

\(\frac{x-3}{x+3}-\frac{x+3}{x-3}=\frac{48}{7},x\neq3,x\neq-3\)

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.

\(\frac{x-3}{x+3}-\frac{x+3}{x-3}=\frac{48}{7},x\neq3,x\neq-3\)

Taking L.C.M

Cross Multiplying we get, 

⇒ 7(2 x² + 18) = 48(x² – 9) 

⇒ -84x = 48x2 – 432 

⇒ 4x² + 7x – 36 = 0 

⇒ 4x² + 16x – 9x – 36 = 0 

⇒ 4x(x + 4) -9(x + 4) = 0 

⇒ (4x – 9)(x + 4) = 0 

⇒ x = 9/4, -4