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Solve the following quadratic equations by factorization:\(\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}\) |
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. \(\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}\) ⇒ 4(x2 + 3x + (x – 1)(x – 2)) = 17(x2 – 2x) ⇒ 4(x2 + 3x + x2 – 3x + 2) = 17(x2 – 2x) ⇒ 8x2 + 8 = 17x2 – 34x ⇒ 9x2 – 34x – 8 = 0 ⇒ 9x2 – 36x + 2x – 8 = 0 ⇒ 9x(x – 4) + 2(x – 4) = 0 ⇒ (9x + 2)(x – 4) = 0 ⇒ x = -2/9, 4 |
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