Answer:
please see answer below
Explanation:
1/2x - 2/(x-1)
cross-multiply: (meaning multiply top of left with bottom of right, and multiply bottom of left with top of right. mulitiply both on the bottom to get a 'common denominator')
[(1 (x-1) - 2(2x)] ÷ (2x(x-1))
[x -1 - 4x] ÷ [2x² - 2x]
[-3x - 1] ÷ [2x² - 2x].
this is 1/2x - 2/(x-1) in the question.
so, [-3x - 1] ÷ [2x² - 2x] = -2÷ 5.
again, cross-multiply: no common denominator required this time
[5(-3x - 1)] = [-2(2x² - 2x)]
simplify:
-15x - 5 = - 4x² + 4x
collect 'like' terms by moving -4x² + 4x to the other side:
4x² - 4x - 15x - 5 = 0
4x² - 19x - 5 = 0.
use the quadratic formula:
x = [(-b ± √(b² - 4ac)) ÷ 2a]
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
x = [(-(-19) ± √((-19)² - 4(4)(-5))) ÷ 2(4)]
= [(19 ± √(361 + 80)) ÷ 8]
= [(19 ± √(441)) ÷ 8]
= [(19 ± 21) ÷ 8]
= 40/8 or -2/8
= 5 or -0.25