How do you solve #\frac { - 3} { x + 7} = \frac { 8} { x - 4}#?

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Answer 1 · 2016-11-06T04:53:21

#x=4#

#-3(x-4)=8(x-7)#
#-3x+12=8x+56#
#12-56=8x+3x#
#-44=11x#
#x=-44/11#
#x=-44/11#

here x can never be 0 or -7 as these can make denominators zero

Answer 2 · 2016-11-06T05:06:55

#x=-4#

#(-3)/(x+7)=8/(x-4)#

Cross multiply.

#-3(x-4)=8(x+7)#

Expand both sides.

#-3x+12=8x+56#

Add #3x# to both sides.

#12=8x+56+3x#

#12=11x+56#

Subtract #56# from both sides.

#12-56=11x#

#-44=11x#

Divide both sides by #11#.

#-44/11=x#

#-4=x#

Switch sides.

#x=-4#