How do you simplify $\frac { x + 2} { ( x - 3) ( x + 1) } + \frac { x ( x - 2) } { 3( x - 3) } + \frac { 1- x ^ { 3} } { 3( x ^ { 2} - 2x - 3) } = - \frac { x } { 3( x + 1) }$ ?

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Answer 1 · 2018-07-07T12:21:11

$x=7/2$

$(x+2)/((x-3)(x+1))+(x(x-2))/(3*(x-3))+(1-x^3)/(3*(x^2-2x-3))=-x/(3*(x+1))$

$(3*(x+2)+x(x-2)(x+1)+1-x^3)/(3*(x^2-2x-3))=-x/(3*(x+1))$

$(3x+6+x^3-x^2-2x+1-x^3)/(3*(x^2-2x-3))=-x/(3*(x+1))$

$(-x^2+x+7)/(3*(x^2-2x-3))=-x/(3*(x+1))$

$(-x^2+x+7)/(x^2-2x-3)=-x/(x+1)$

$-(x^2-x-7)/((x+1)*(x-3))=-x/(x+1)$

$(x^2-x-7)/((x+1)*(x-3))=x/(x+1)$

$x^2-x-7=x*(x-3)$

$x^2-x-7=x^2-3x$

$2x=7$ , so $x=7/2$