Question

Solve the quadratic equation using factorization method
4/X+2-1/X+3=4/2x+1

Answer 1

Step-by-step explanation:

$\frac{4}{x + 2} - \frac{ 1}{x + 3} = \frac{4}{2x + 1} \\ \\ \frac{4(x + 3) - 1(x + 2)}{(x + 2)(x + 3)} = \frac{4}{2x + 1} \\ \\ \frac{4x + 12 - x - 2}{ {x}^{2} + 3x + 2x + 6 } = \frac{4}{2x + 1} \\ \\ \frac{3x + 10}{ {x}^{2} + 5x + 6} = \frac{4}{2x + 1} \\ \\ (3x + 10)(2x + 1) = 4( {x}^{2} + 5x + 6) \\ \\ 6 {x}^{2} + 3x + 20x + 10 = 4 {x}^{2} + 20x + 24 \\ \\ 6{x}^{2} + 23x + 10 = 4 {x}^{2} + 20x + 24 \\ \\ 4 {x}^{2} + 3x - 14 = 0 \\ \\ by \: quadratic \: equation..... \\ \\ \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \frac{ - 4 \binom{ + }{ - } \sqrt{9 - 4(4)( - 14)} }{8} \\ \\ \frac{ - 4 \binom{ + }{ - } 15.26 }{8} \\ \\ \frac{ - 4 + 15.26}{8} .......... \frac{ - 4 - 15 .26}{8} \\ \\ \frac{11.26}{8} ......... \frac{ - 19.26}{8} \\ \\ \frac{11}{8} ......... \frac{19}{8} ......(approx)$

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