How do you solve #2/3 = 2 - (5x-3)/(x-1)#?

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Answer 1 · 2016-03-30T13:33:58

#x=5/11#

We have #2/3=2/1-(5x-3)/(x-1)#

We need a common denominator to apply the subtraction on the right.

If we multiply a number by 1 we do not change its value. However, 1 can come in many forms. Examples: #3/3" ; "(5b)/(5b)" ; "(x-1)/(x-1)#

Multiply #2/1# by 1 but in the form of #1=(x-1)/(x-1)# giving

#" "2/3= (2/1xx(x-1)/(x-1)) -(5x-3)/(x-1)#

#" "2/3 = (2(x-1)-(5x-3))/(x-1)#

#" "2/3=(2x-2-5x+3)/(x-1)#

#" "2/3=(-3x+1)/(x-1)#

#" "2(x-1)=3(-3x+1)#

#" "2x-2=-9x+3#

#" "11x=5#

#" "x=5/11#