Question

Solve and check (c−4 / c−2c+2 )−2=0. The solution is c=______. How many extraneous solutions are there?

a) c=2, no extraneous solutions
b) c=3, one extraneous solution
c) c=4, two extraneous solutions
d) c=5, cannot be determined

Answer 1

After simplifying and solving the equation assuming a typo in the original, the solution for c is 8/3. Without the exact form of the original question, we cannot determine the number of extraneous solutions.

Step-by-step explanation:

To solve the equation (c-4)/(c-2c+2)-2=0, we need to simplify and solve for c. The equation can be rewritten as (c-4)/(c-(2c-2))-2=0. First, we simplify the denominator: (c-(2c-2)) becomes (-c+2), making our equation (c-4)/(-c+2)-2=0. Now, we solve for c:

(c-4)/(-c+2) = 2

c-4 = -2c + 4

c + 2c = 4 + 4

3c = 8

c = 8/3

Assuming there is a typo in the original equation and that we have the correct form, the solution is c = 8/3. However, without knowing the exact form of the original question, we cannot determine the number of extraneous solutions.