How Do You Solve This? 2/3=2- (5x-3)/(x-1) Please Show Work

2 Answers

Oddman Profile
Oddman answered
(2/3) = 2 - (5x-3)/(x-1)
2(x-1) = 6(x-1) - 3(5x-3)    (multiply both sides by 3(x-1), the least common denominator)
2x -2 = 6x -6 -15x + 9    (use the distributive property to eliminate parentheses)
11x -2 = 3    (add 9x to both sides, collect terms)
11x = 5    (add 2 to both sides)
x = 5/11    (divide both sides by 11)

Check
2/3 = 2 - (5(5/11)-3)/((5/11)-1)
2/3 = 2 - (25/11 -33/11)/(5/11 -11/11)
2/3 = 2 - (-8/11)/(-6/11)
2/3 = 2 - 4/3
2/3 = 6/3 - 4/3    (yes)

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Anonymous