Question

Solve the equation.
$(2x + 1) + \frac{3}{2x + 1} = 4$
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Answer 1

$\huge{\underline{\underline{\mathfrak{\red{Solution:}}}}}$

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${4x}^{2} + 4x + 1 + 3 = 4(2x + 1)$

${(2x + 1)}^{2} + 3 = 4(2x + 1)$

$4( {x}^{2} + x + 1) = 4(2x + 1)$

${x}^{2} + x + 1 = 2x + 1$

$x = 1$

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$\huge{\underline{\underline{\mathfrak{\green{Thanks\:on\:my\:Answer}}}}}$

Answer 2

$\huge\underline\mathbb\color{lightpink}SOLUTION$

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$(2x + 1) + \frac{3}{2x + 1} = 4 \\ \implies \: \frac{2x + {1})^{2} }{2x + 1} = \frac{4}{1} \\ \implies \frac{4 {x}^{2} + 4x + 1 + 3 }{2x + 1} = 4 \\ \implies \frac{4( {x}^{2} + x + 1) }{2x + 1} = 4 \\ \implies {x}^{2} + x + 1 = 2x + 1 \\ \implies {x}^{2} + x - 2 = 1 - 1 \\ \implies {x}^{2} - x = 0 \\ \implies \: x(x - 1) = 0 \\ \\ Either \: \\ x =0 \\ \\ Or \: \\ x - 1 = 0 \\ \implies \: x = 1$

The solution is x= 0,1

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