What is the solution of StartFraction 1 Over c minus 3 EndFraction minus StartFraction 1 Over c EndFraction = StartFraction 3 Over c (c minus 3) EndFraction?
c = 0 and c = 3
all real numbers
all real numbers, except c ¹ 0 and c ¹ 3
no solution

Explanation:

The equation is:

Since c - 3, c, and c(c - 3) are he denominators, none of them can be equal to zero:

Now you can multiply both sides of the equation by the common denominator: c (c - 3):

That means the equality is valid for all real numbers for which it is defined, which is all real numbers except c = 0 and c = 3.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.