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# How do you solve the rational equation 5/(-x-6)=2/x ?

Feb 15, 2016

$x = - \frac{12}{7}$

#### Explanation:

color(blue)(5/(-x-6)=2/x

Cross multiply color(brown)(a/b=c/d,ad=bc

$\rightarrow 5 x = 2 \left(- x - 6\right)$

Use distributive property $\textcolor{\mathmr{and} a n \ge}{a \left(b + c\right) = a b + a c}$:

$\rightarrow 5 x = - 2 x - 12$

Add $2 x$ both sides:

$\rightarrow 5 x + 2 x = - 12$

$\rightarrow 7 x = - 12$

Divide $7$ both sides:

$\rightarrow \frac{7 x}{7} = - \frac{12}{7}$

$\rightarrow \frac{\cancel{7} x}{\cancel{7}} = - \frac{12}{7}$

rArrcolor(green)(x=-12/7

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