How do you solve $x - \frac{3 x}{2} = \frac{x + 7}{x - 11}$ $x-(3x)/(2)=(x+7)/(x-11)$ ?

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Answer 1 · 2015-05-08T20:17:38

$x - \frac{3 x}{2} = \frac{x + 7}{x - 11}$ $x-(3x)/2 = (x+7)/(x-11)$

Simplify the left side of the equation:
$- \frac{x}{2} = \frac{x + 7}{x - 11}$ $-x/2 = (x+7)/(x-11)$

Multiply both sides by $(- 2) (x - 11)$ $(-2)(x-11)$
$x^{2} - 11 x = - 2 x - 14$ $x^2-11x = -2x-14$

Re-arrange terms to the left side
$x^{2} - 9 x + 14 = 0$ $x^2-9x +14 = 0$

Factor
$(x - 7) (x - 2) = 0$ $(x-7)(x-2)=0$

State solutions:
$x = 7$ $x=7$ or $x = 2$ $x=2$

How do you solve x−3x2=x+7x−11x-(3x)/(2)=(x+7)/(x-11)?