Question

1/x-3+2/x-2=8/x
factorise this

Answer 1

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Answer 2

Answer:

$\implies x = 4 \: Or \: x =\frac{12}{5}$

Step-by-step explanation:

$Given \: \frac{1}{x-3}+\frac{2}{x-2}=\frac{8}{x}$

$\implies \frac{x-2+2(x-3)}{(x-3)(x-2)}=\frac{8}{x}$

$\implies \frac{x-2+2x-6}{x^{2}-5x+6}=\frac{8}{x}$

$\implies x(3x-8)=8(x^{2}-5x+6)$

$\implies 3x^{2}-8x=[tex]=8x^{2}-40x+48$

$\implies 0=8x^{2}-40x+48-3x^{2}+8x$

$\implies</p><p> 5x^{2}-32x+48=0$

Splitting the middle term,we get

$\implies 5x^{2}-20x-12x+48=0$

$\implies 5x(x-4)-12(x-4)=0$

$\implies (x-4)(5x-12)=0$

$\implies x-4=0 \:Or \: 5x-12=0$

$\implies x = 4 \: Or \: x =\frac{12}{5}$

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