Question

Factorise using factorisation​

Answer 1

Answer:

$\frac{x - 3}{x - 2} - \frac{1 - x}{x} = \frac{17}{4} \\ cross \: multipliction \\ \frac{x(x - 3) - (x - 2)(1 - x)}{x(x - 2)} = \frac{17}{4} \\ \frac{ {x}^{2} - 3x - (x - {x}^{2} - 2 + 2x) }{ {x}^{2} - 2x } = \frac{17}{4} \\ \frac{ {x}^{2} - 3x - ( - {x}^{2} + x - 2) }{ {x}^{2} - 2x } = \frac{17}{4} \\ \frac{ {x}^{2} - 3x + {x}^{2} - x + 2 }{ {x}^{2} - 2x } = \frac{17}{4} \\ \frac{2 {x}^{2} - 4x + 2 }{ {x}^{2} - 2x } = \frac{17}{4} \\ 4(2 {x}^{2} - 4x + 2) = 17( {x}^{2} - 2x) \\ 8 {x}^{2} - 16x + 8 = 17 {x}^{2} - 34x \\ 17 {x}^{2} - 8 {x}^{2} - 34x + 16x - 8 = 0 \\ 9 {x}^{2} - 18x - 8 = 0 \\ by \: factorisation \\ 9 {x}^{2} - 12x - 6x + 8 = 0 \\ 3x(3x - 4) - 2(3x - 4) = 0 \\ 3x - 2 = 0 \: \: or \: \: 3x - 4 = 0 \\ 3x = 2 \: \: or \: \: 3x = 4 \\ x = \frac{2}{3} \: \: or \: \: x = \frac{4}{3}$

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Answer 2

Answer:

Step-by-step explanation:

Refer to the attachment above ♡

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