Question

factorise x-3/x-2 - 1-x/x = 17/4​

Answer 1

Answer:

sorry typing mistake so I could not write the answer properly and next l write properly

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Answer 2

this x+3/x-2.../4 not x-3....plz correction it... OK.. so let's start.....

$we \: have \\ \frac{x + 3}{x - 2} - \frac{1 - x}{x} = \frac{17}{4} \\ = \frac{x(x + 3) - (x - 2)(1 - x)}{x(x - 2)} = \frac{17}{4} \\ = \frac{ {x}^{2} + 3x - (x - {x}^{2} - 2 + 2x) }{ {x}^{2} - 2x} \\ = \frac{ {x}^{2} + 3x - x + {x}^{2} + 2 - 2x}{ {x}^{2} - 2x } \\ = \frac{ {2x}^{2} + 2}{ {x}^{2} - 2x } = \frac{17}{4} \\ \\ = 4( {2x}^{2} + 2) = 17( {x}^{2} - 2x) \\ = 8 {x}^{2} + 18 = 17 {x}^{2} - 34x \\ = 8 {x}^{2} + 8 = 17 {x}^{2} - 34x \\ = (17 - 8) {x}^{2} - 34x \\ = (17 - 8) {x}^{2} - 34x - 8 = 0 \\ = 9 {x}^{2} - 34x - 8 = 0$

[9x-8= -7=>-72=>-36*2 and -34= -36+2]

$= 9 {x}^{2} - 36x + 2x - 8 = 0 \\ = 9x(x - 4) + 2(x - 4) = 0 \\ = (x - 4)(9x + 2) = 0 \\ = (x - 4) = 0 \: or \: 9x + 2 = 0 \\ = x = 4 \: or \: x = \: - \frac{8}{9}$

x=4 and x= -8/9 are the two roots of the given equations.