How do you solve #7/(x+2)= 2/(x-5)#?

1 Answer
Alan P.
May 2, 2016

#x=39/5=7 4/5#

Explanation:

Given
#color(white)("XXX")7/(x+2)=2/(x-5)color(white)("XXX")#note: this equation implies #x!=-2# and #x!=5#

Multiply both sides by #(x+2)(x-5)# (sometimes this will be called "cross multiplying")
#color(white)("XXX")7(x-5)=2(x+2)#
simplify:
#color(white)("XXX")7x-35=2x+4#
subtract #2x# from both sides and add #35# to both sides
#color(white)("XXX")5x=39#
divide both sides by #5#
#color(white)("XXX")x=39/5#

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