How do you solve # ( x+12 )/( x-4 ) = ( x-3 )/( x-7 ) #?

2 Answers
Apr 7, 2018

Answer:

#x=8#

Explanation:

First, we'll cross multiply: if #a/b=c/d# then #a*d=b*c#

#(x+12)(x-7) = (x-4)(x-3)#

Expand

#x^2+5x-84=x^2-7x+12#

Add 84 to both sides and simplify

#x^2+5x cancel(-84 + 84) = x^2-7x+12+84#
#x^2+5x=x^2-7x+96#

Subtract #x^2-7x# from both sides and simplify

#x^2+5x-(x^2-7x)=x^2-7x+96-(x^2-7x)#
#12x=96#

Divide both sides by 12 and simplify

#(cancel(12)x)/cancel(12)=96/12#
#x=8#

~ Alex

Apr 7, 2018

Answer:

#x = 8#

Explanation:

To solve this, we use cross multiplication:
study.com

Based on this, in this case you would do:
#(x+12)(x-7) = (x-3)(x-4)#

And now we just expand and simplify:
#x^2 + 12x - 7x - 84 = x^2 - 3x - 4x + 12#

Combine like terms:
#x^2 + 5x - 84 = x^2 - 7x + 12#

Subtract #x^2# on both sides of the equation:
#x^2 color(red)(-x^2) + 5x - 84 = x^2 color(red)(-x^2) - 7x + 12 #

#5x - 84 = -7x + 12#

Add #7x# to both sides of the equation:
#5x color(red)(+ 7x) - 84 = -7x color(red)(+7x) + 12#

#12x - 84 = 12#

Add #84# to both sides of the equation:
#12x - 84 color(red)(+ 84) = 12 color(red)(+ 84)#

#12x = 96#

Divide both sides by #12#:
#x = 8#

Hope this helps!