Question

X-2/x+2+6(x-2/x-6)=1 xnot equal to -2 6

Answer 1

Simplify:

Step-by-step explanation:

$\ Given \ value: \\\\\frac{x-2}{x+2}+2+6\frac{(x-2)}{(x-6)} =1 \\\\\ Solution:\\\\\frac{x-2}{x+2}+2+6\frac{(x-2)}{(x-6)} =1 \\\\\rightarrow \frac{(x-2)(x-6)+2(x+2)(x-6)+6(x-2)(x+2)}{(x+2)(x-6)} =1 \\\\\rightarrow \frac{x^2-6x-2x+12+2(x^2-6x+2x-12)+6(x^2+2x-2x-4)}{(x+2)(x-6)} =1 \\\\\rightarrow \frac{x^2-8x+12+2(x^2-4x-12)+6(x^2-4)}{(x^2-6x+2x-12)} =1 \\\\\rightarrow \frac{x^2-8x+12+2x^2-8x-24+6x^2-24}{(x^2-4x-12)} =1 \\\\\rightarrow \frac{9x^2-16x-36}{(x^2-4x-12)} =1$

$\rightarrow 9x^2-16x-36=x^2-4x-12 \\\\\rightarrow 9x^2-16x-36-x^2+4x+12=0 \\\\\rightarrow 8x^2-12x-24 =0\\\\\rightarrow 4(2x^2-3x-6 )=0\\\\ \rightarrow 2x^2-3x-6 =0$

$\ compare \ the \ value\ with \ ax^2+bx+c=0 \\\\a=2\\b=-3\\c=-6$

$\ formula: \\\\x= \frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\\put \ the \ value \ in \ above \ formula\\\\ x= \frac{-(-3)\±\sqrt{(-3)^2-4.2.(-6)}}{2.2} \\\\x= \frac{3\±\sqrt{9+48}}{4}\\x= \frac{3\±\sqrt{57}}{4}$

So the the x is not equal to -2 , 6.

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