Question

solve quadratic equation. X+3/x-2 -1-x/x =17/4 by factorisation method

Answer 1

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Answer 2

Answer:

$x = 4 \: Or \: x = \frac{-2}{9}$

Step-by-step explanation:

$We \: have \: a \: \\quadratic\: equation\:\\\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$

$\implies \frac{[x(x+3)-(x-2)(1-x)]}{(x-2)x}=\frac{17}{4}$

$\implies \frac{(x^{2}+3x-(x-x^{2}-2+2x)}{x^{2}-2x}=\frac{17}{4}$

$\implies \frac{x^{2}+3x-3x+x^{2}+2}{x^{2}-2x}=\frac{17}{4}$

$\implies \frac{2x^{2}+2}{x^{2}-2x}=\frac{17}{4}$

\* Do the cross multiplication, we get

$\implies 4(2x^{2}+2)=17(x^{2}-2x)$

$\implies 8x^{2}+8=17x^{2}-34x$

$\implies 17x^{2}-34x-8x^{2}-8=0$

$\implies 9x^{2}-34x-8=0$

/* Splitting the middle term, we get

$\implies 9x^{2}-36x+2x-8=0$

$\implies 9x(x-4)+2(x-4)=0$

$\implies (x-4)(9x+2)=0$

$\implies (x-4)=0\: Or \: 9x+2=0$

$\implies x = 4 \: Or \: x = \frac{-2}{9}$

Therefore,

$x = 4 \: Or \: x = \frac{-2}{9}$