How do you multiply $\frac{2 x}{x + 2} - 2 = \frac{x - 8}{x - 2}$ $(2x) / (x+2) - 2 = (x-8) / (x-2)$ ?

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Answer 1 · 2018-08-12T16:53:22

$x = - 4 or x = 6$ $x=-4 or x=6$

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

$:.=(2x(x-2)-2(x+2)(x-2)=(x+2)(x-8))/((x+2)(x-2))$

Multiply both sides by $(x+2)(x-2)$

$:.=2x(x-2)-2(x+2)(x-2)=(x+2)(x-8)$

$:.=2x^2-4x-2x^2+8=x^2-6x-16$

$:.=2x^2-x^2-2x^2-4x+6x+8+16=0$

$:.=-x^2+2x+24=0$

multiply both sides by $-1$

$:.=x^2-2x-24=0$

$:.=(x+4)(x-6)=0$

$:.=x=-4 or x=6$

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check:-

substitute $x=-4$

$:.=(2(-4))/((-4)+2)-2=((-4)-8)/((-4)-2)$

$:.=(-8)/-2-2=(-12)/-6$

$:.=4-2=2$

substitute $x=6$

$(2(6))/((6)+2)-2=((6)-8)/((6-2))$

$:.=12/8-2=(-2)/4$

$:.=3/2-2=-1/2$

$1 1/2-2=-1/2$

$:.=-1/2=-1/2$

How do you multiply (2x) / (x+2) - 2 = (x-8) / (x-2)2xx+2−2=x−8x−2(2x) / (x+2) - 2 = (x-8) / (x-2)?