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Solve the following quadratic equations by factorization:\(\frac{2}{x + 1}+\frac{3}{2(x-2)}=\frac{23}{5x};x\neq0,-1,2\) |
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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 \(\frac{2}{x + 1}+\frac{3}{2(x-2)}=\frac{23}{5x};x\neq0,-1,2\) ⇒ 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 |
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