Solve x = (3x + 1)/(4x) by factorisation

Given, ⇒ ⇒ x.4x = 3x + 1 ⇒ 4x 2 = 3x + 1 ⇒ 4x 2 - 3x - 1 = 0 ⇒ 4x 2 - 4x + x - 1 = 0 ⇒ 4x(x - 1) + 1(x - 1) = 0 ⇒ (4x + 1)(x - 1) = 0 ⇒ (4x + 1) = 0 or (x - 1) = 0 ⇒ 4x = -1 or x = 1 ⇒ x = or x = 1. Hence, x = or x = 1.

Mathematics

Solve the following equation by factorisation:
x = $\dfrac{3x + 1}{4x}$

Quadratic Equations

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Answer

Given,

⇒ $x = \dfrac{3x + 1}{4x}$

⇒ x.4x = 3x + 1

⇒ 4x² = 3x + 1

⇒ 4x² - 3x - 1 = 0

⇒ 4x² - 4x + x - 1 = 0

⇒ 4x(x - 1) + 1(x - 1) = 0

⇒ (4x + 1)(x - 1) = 0

⇒ (4x + 1) = 0 or (x - 1) = 0

⇒ 4x = -1 or x = 1

⇒ x = $-\dfrac{1}{4}$ or x = 1.

Hence, x = $-\dfrac{1}{4}$ or x = 1.

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