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Solve the following quadratic equations by factorization:\(\frac{4}{x}-3=\frac{5}{2x+3},x\neq0,-\frac{3}{2}\) |
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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. \(\frac{4}{x}-3=\frac{5}{2x+3},x\neq0,-\frac{3}{2}\) ⇒ (4 – 3x)(2x + 3) = 5x ⇒ 8x + 12 – 6x2 – 9x = 5x ⇒ 6x2 + 6x – 12 = 0 ⇒ x2 + x – 2 = 0 ⇒ x2 + 2x – x – 2 = 0 ⇒ x(x + 2) – (x + 2) = 0 ⇒ (x – 1)(x + 2) = 0 ⇒ x = 1, - 2 |
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