Question

5/2x+1 + 6/x+1 = 3 factorise the following

Answer 1

Answer:

$\frac{5}{2x + 1} + \frac{6}{x + 1} = 3 \\ \\ \\ \frac{5(x + 1) + 6(2x + 1)}{(2x + 1)(x + 1)} = 3 \\ \\ \\ \\ \frac{5x + 5 + 12x + 6}{ {2}x^{2} + 2x + x + 1} = 3 \\ \\ \\ \\ 17x + 11 = 6 {x}^{2} + 9x + 3 \\ \\ \\ 8x + 8 = 6 {x}^{2} \\ \\ 4x + 4 = 3 {x}^{2} \\ \\ \\ 3 {x}^{2} - 4x - 4 = 0 \\ \\ 3 {x}^{2} - 6x + 2x - 4 = 0 \\ \\ \\ 3x(x - 2) + 2(x - 2) = 0 \\ \\ \\ (3x + 2)(x - 2) = 0 \\ \\ 3x + 2 = 0 \\ \\ x = \frac{ - 2}{3} \\ \\ \\ \\ x - 2 = 0 \\ \\ x = 2$

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