We want to solve the given rational equation.
2/c-2=2-4/c
For simplicity, we will start by replacing the variable c with the variable x.
2/c-2=2-4/c c= x ⟶ 2/x-2=2-4/x
Let's begin by highlighting all of the different factors in the denominators. This will help us find the least common denominator (LCD).
2/x-2=2-4/x
We will solve the equation by multiplying each side by the LCD to clear denominators.
Note that we have a quadratic equation now. Let's identify the values of a, b, and c.
x^2-5x+4=0 ⇔ 1x^2 +( -5)x+4=0
We have that a= 1, b= -5, and c=4. Let's substitute these values into the Quadratic Formula and solve for x.
Let's calculate both solutions by using the positive and negative signs.
x=5± 3/2
x=5+ 3/2
x=5- 3/2
x=8/2
x=2/2
x=4
x=1
Therefore, the solutions are x=4 and x=1. Recall that, at the beginning of the solution, we substituted x for c. Therefore, the solutions to the original equation are c=4 and c=1.
x=4 &x=c ⟶ c=4 [0.69em]
x=1 &x=c ⟶ c=1
Let's check them to see if we have any extraneous solutions. To do this, we need to substitute 4 and 1 for c in the original equation. Let's start with c=4.
