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Solve the following quadratic equations by factorization:\(\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=\frac{5}{2}, x\neq-\frac{1}{2},1\)

Answer»

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.

\(\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=\frac{5}{2}, x\neq-\frac{1}{2},1\)

⇒ 2(x2 - 2x + 1 + 4x2 + 4x + 1) = 5(2x2 – x – 1) 

⇒ 10x2 + 4x + 4 = 10x2 – 5x – 5 

⇒ 9x = -9 

⇒ x = -1



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