Question
Solve equation using factorisation method:
$x=\frac{3 x+1}{4 x}$
$x=\frac{3 x+1}{4 x}$
✓
Answer
$x=\frac{3 x+1}{4 x}$
⇒ 4x2 = 3x + 1
⇒ 4x2 - 3x - 1 = 0
⇒ 4x2 - 4x + x - 1 = 0
⇒ 4x( x -1) +1 (x -1) = 0
⇒ (x -1)(4x + 1) = 0
since x -1=0 or 4x + 1= 0
then $x=1$ or $x=\frac{-1}{4}$
⇒ 4x2 = 3x + 1
⇒ 4x2 - 3x - 1 = 0
⇒ 4x2 - 4x + x - 1 = 0
⇒ 4x( x -1) +1 (x -1) = 0
⇒ (x -1)(4x + 1) = 0
since x -1=0 or 4x + 1= 0
then $x=1$ or $x=\frac{-1}{4}$
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