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

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Answer 1 · 2016-02-15T12:41:33

#x=-12/7#

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

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

#rarr5x=2(-x-6)#

Use distributive property #color(orange)(a(b+c)=ab+ac)#:

#rarr5x=-2x-12#

Add #2x# both sides:

#rarr5x+2x=-12#

#rarr7x=-12#

Divide #7# both sides:

#rarr(7x)/7=-12/7#

#rarr(cancel7x)/cancel7=-12/7#

#rArrcolor(green)(x=-12/7#