Question

(1-2x)+(1+2x)/(4x+1)+(x-3)=1/2​

Answer 1

Solution

Step by step Explanation:

$\sf\longmapsto(1 - 2x) + \dfrac{1 + 2x}{4x + 1} + (x - 3) = \dfrac{1}{2}$

$\sf\longmapsto \dfrac{(1 - 2x)(4x + 1) + 1 + 2x + (4x + 1)(x - 3)}{4x + 1} = \dfrac{1}{2}$

$\sf\longmapsto4x + 1 - 8 {x}^{2} - 2x + 1 + 2x + 4 {x}^{2} - 12x + x - 3 = \dfrac{1}{2} (4x + 1)$

$\sf\longmapsto - 4 {x}^{2} - 7x - 1 = \dfrac{4x + 1}{2}$

$\sf\longmapsto4x + 1 = - 8 {x}^{2} - 14x - 2$

$\sf\longmapsto - 8 {x}^{2} - 18x - 3 = 0$

$\sf\longmapsto8 {x}^{2} + 18x + 3 = 0$

Here ,we use quadratic formula for further factorise:

$\sf \boxed{x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}}$

$\sf\longmapsto \: x = \dfrac{ - 18 \pm \sqrt{ {(18)}^{2} - 4(8)(3)} }{2 \times 8}$

$\sf\longmapsto \: x = \dfrac{ - 18 \pm \sqrt{324 - 96} }{16}$

$\sf\longmapsto \: x = \dfrac{ - 18 \pm \sqrt{228} }{16}$

$\sf\longmapsto \: x = \dfrac{2( - 9 \pm2 \sqrt{57} )}{16} = \dfrac{ - 9 \pm \sqrt{57} }{8}$

Answer 2

Answer:

always be happy☺️☺️☺️

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