Question

please help me ❤️❤️❤️​

Answer 1

$\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3} \\ \frac{(x - 1)(x - 4) + (x - 3)(x - 2)}{(x - 2)(x - 4)} = \frac{10}{3} \\ \frac{ {x}^{2} - 4x - x + 4 + {x}^{2} - 2x - 3x + 6}{ {x}^{2} - 4x - 2x + 8} = \frac{10}{3} \\ \frac{2 {x}^{2} - 10x + 10}{ {x}^{2} - 6x + 8} = \frac{10}{3} \\ now \: cross \: multiply : \\ 3(2 {x}^{2} - 10x + 10) = 10({x}^{2} - 6x + 8) \\ 6 {x}^{2} - 30x + 30 = 10 {x}^{2} - 60x + 80 \\ 0 = 10 {x}^{2} - 6 {x}^{2} - 60x + 30x + 80 - 30 \\ 0 = 4 {x}^{2} - 30x + 50 \\ 0 = 4 {x}^{2} - 20x - 10x + 50 \\ 0 = 4x (x - 5) - 10(x - 5) \\ 0 = (4x - 10)(x - 5) \\ x = \frac{10}{4} = \frac{5}{2} \: , \: 5$

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Answer 2

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