How do you solve #x/(x-1)>2#?

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Answer 1 · 2017-02-18T02:30:59

#1< x < 2 # or in interval form: #(1, 2)#

Put the inequality in #> 0# form:

#x/(x-1) -2 > 0#

Find the common denominator:

#x/(x-1) + (-2(x-1))/(x-1) > 0#;

Remember: #-2(x-1) = -2x+2#

Combine under the same denominator:

#(x -2x+2)/(x-1) = (-x+2)/(x-1) > 0#

Key Points: #-x+2 > 0# and #x-1 >0#

Simplify: #-x > -2# and #x > 1#

When you divide by -1, the inequality changes direction:
#(-x/-1) < (-2/-1); x < 2#

Therefore: #1 < x < 2# or in interval form: #(1, 2)#