Question

4/x^2+5x+6 -3/x+3 =1/2

Answer 1

$\\ \frac{4}{ {x}^{2} + 5x + 6} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{ {x}^{2} + 2x + 3x + 6 } - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{x(x + 2) + 3(x + 2)} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{(x + 2)(x + 3)} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4 - 3(x + 2)}{(x + 2)(x + 3)} = \frac{1}{2}$

$\\ = > \frac{4 - 3x - 6}{ {x}^{2} + 5x + 6 } = \frac{1}{2}$

$\\ = > \frac{ - \: 3x - 2}{ {x }^{2} + 5x + 6 } = \frac{1}{2}$

$\\ = > {x}^{2} + 5x + 6 = - 6x - 4$

$\\ = > {x}^{2} + 5x + 6 + 6x + 4 = 0$

$\\ = > {x}^{2} + 11x + 10 = 0$

$\\ = > {x}^{2} + x + 10x + 10 = 0$

$\\ = > x(x + 1) + 10(x + 1) = 0$

$\\ = > (x + 1) \: (x + 10) = 0$

$\\ = > x + 1 = 0 \: \: \: or, \: x + 10 = 0$

$\\:- \: \: \: x = - 1 \: \: \: \: \: :- \: \: \: x = - 10$

$\\ The \: value \: of \: x \: = - 1 \: \: or \: -10$

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

Answer:

$\\ \frac{4}{ {x}^{2} + 5x + 6} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{ {x}^{2} + 2x + 3x + 6 } - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{x(x + 2) + 3(x + 2)} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4}{(x + 2)(x + 3)} - \frac{3}{x + 3} = \frac{1}{2}$

$\\ = > \frac{4 - 3(x + 2)}{(x + 2)(x + 3)} = \frac{1}{2}$

$\\ = > \frac{4 - 3x - 6}{ {x}^{2} + 5x + 6 } = \frac{1}{2}$

$\\ = > \frac{ - \: 3x - 2}{ {x }^{2} + 5x + 6 } = \frac{1}{2}$

$\\ = > {x}^{2} + 5x + 6 = - 6x - 4$

$\\ = > {x}^{2} + 5x + 6 + 6x + 4 = 0$

$\\ = > {x}^{2} + 11x + 10 = 0$

$\\ = > {x}^{2} + x + 10x + 10 = 0$

$\\ = > x(x + 1) + 10(x + 1) = 0$

$\\ = > (x + 1) \: (x + 10) = 0$

$\\ = > x + 1 = 0 \: \: \: or, \: x + 10 = 0$

$\\:- \: \: \: x = - 1 \: \: \: \: \: :- \: \: \: x = - 10$

$\\ The \: value \: of \: x \: = - 1 \: \: or \: -10$

I hope this will help you dear..

Always stay safe and stay healthy..