Question

X+1/X+3=3x+2/2x+3 : solve it using quadratic equations..help me it's urgent.​

Answer 1

Answer:

- 3 + √6 & - 3 - √6

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Step-by-step explanation:

$\frac{x + 1}{x + 3} = \frac{3x + 2}{2x + 3} \\ (after \: cross \: multiplication) \\ = > x + 1(2x + 3) = x + 3(3x + 2) \\ = > x(2x + 3) + 1(2x + 3) = x(3x + 2) + 3(3x + 2) \\ = > 2 {x }^{2} + 3x + 2x + 3 = {3x}^{2} + 2x + 9x + 6 \\ = > {2x}^{2} + 5x + 3 = {3x}^{2} + 11x + 6 \\ = > 5x + 3 = {3x}^{2} - {2x}^{2} + 11x + 6 \\ = > 3 = {x}^{2} + 11x - 5x + 6 \\ = > 0 = {x}^{2} + 6x + 6 - 3 \\ = > {x}^{2} + 6x + 3 = 0$

Now it is the standard form of quadratic equation (ax² + bx + c), here

a = 1

b = 6

c = 3

We will find the roots of the quadratic equation,

$roots \: = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} \\ = > \frac{ - 6 ± \sqrt{( {6)}^{2} - 4(1)(3)} }{2(1)} \\ = > \frac{ - 6 ± \sqrt{36 - 12} }{2} \\ = > \frac{ - 6 ± \sqrt{24} }{2} \\ = > \frac{ - 6 ± 2 \sqrt{6} }{2} \\ = > - 3 ± \sqrt{6} \\ roots = - 3 + \sqrt{6} \\ - 3 - \sqrt{6}$

Hence the value of x = -3 + √6 & -3 - √6

hope it helps.