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

Answer 1

#x=1/2(1+-sqrt3)#

#(2x)/1=1/(x-1)#

Cross-multiply

#2x(x-1)=1#
#2x^2-2x-1=0#
For a quadratic equation of the form: #ax^2+bx+c#
#x=(-b+-sqrt(b^2-4ac))/(2a)#
In our case: #a=2, b=-2, c=-1#
#:. x=(+2+-sqrt(4+4*2*1))/(2*2)#
#=(+2+-sqrt(12))/(4)#
#=(2+-2sqrt(3))/(4)#
#= 1/2(1+-sqrt3)#
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Answer 2

Multiply through by the denominator of the right-hand side and then solve the resulting quadratic equation.

#x=1.366# or #-0.366#

#(2x)/1# is just #2x#, so
#2x=1/(x-1)#
Multiply both sides by #(x-1)#
#2x(x-1)=1(cancel(x-1))/cancel(x-1)#
#2x^2-2x=1#
#2x^2-2x-1=0#

Now we can use the quadratic formula (or any other method) to solve this quadratic equation.

#x=(-b+-sqrt(b^2-4ac))/(2a)#
#=(2+-sqrt(4+8))/(4)#
#x=1.366# or #-0.366#
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Answer 3

To solve the equation (2x)/1 = 1/(x-1), we can cross-multiply to eliminate the fractions. This gives us 2x(x-1) = 1(1), which simplifies to 2x^2 - 2x = 1. Rearranging the equation, we have 2x^2 - 2x - 1 = 0. To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a), where a = 2, b = -2, and c = -1. Plugging in these values, we get x = (2 ± √(4 - 4(2)(-1)))/(2(2)), which simplifies to x = (2 ± √(4 + 8))/4. Further simplifying, we have x = (2 ± √12)/4, and finally x = (2 ± 2√3)/4. This can be simplified further to x = (1 ± √3)/2. Therefore, the solutions to the equation are x = (1 + √3)/2 and x = (1 - √3)/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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