How do you solve 2/3 = 2 - (5x-3)/(x-1)23=2−5x−3x−1?

1 Answer
Tony B
Mar 30, 2016

x=5/11x=511

Explanation:

We have 2/3=2/1-(5x-3)/(x-1)23=21−5x−3x−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)33 ; 5b5b ; x−1x−1

Multiply 2/121 by 1 but in the form of 1=(x-1)/(x-1)1=x−1x−1 giving

" "2/3= (2/1xx(x-1)/(x-1)) -(5x-3)/(x-1) 23=(21×x−1x−1)−5x−3x−1

" "2/3 = (2(x-1)-(5x-3))/(x-1) 23=2(x−1)−(5x−3)x−1

" "2/3=(2x-2-5x+3)/(x-1) 23=2x−2−5x+3x−1

" "2/3=(-3x+1)/(x-1) 23=−3x+1x−1

" "2(x-1)=3(-3x+1) 2(x−1)=3(−3x+1)

" "2x-2=-9x+3 2x−2=−9x+3

" "11x=5 11x=5

" "x=5/11 x=511

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