QuestionAugust 27, 2025

What is the solution of (1)/(c-3)-(1)/(c)=(3)/(c(c-3)) 7 c=0 and c=3 all real numbers all real numbers, except cneq 0 and cneq 3 no solution

What is the solution of (1)/(c-3)-(1)/(c)=(3)/(c(c-3)) 7 c=0 and c=3 all real numbers all real numbers, except cneq 0 and cneq 3 no solution
What is the solution of (1)/(c-3)-(1)/(c)=(3)/(c(c-3)) 7
c=0 and c=3
all real numbers
all real numbers, except cneq 0 and cneq 3
no solution

Solution
4.7(337 votes)

Answer

All real numbers, except c \neq 0 and c \neq 3 Explanation 1. Simplify the equation Combine fractions on the left side: \frac{1}{c-3} - \frac{1}{c} = \frac{c - (c-3)}{c(c-3)} = \frac{3}{c(c-3)}. 2. Compare both sides Both sides are equal: \frac{3}{c(c-3)} = \frac{3}{c(c-3)}. 3. Identify restrictions Denominator cannot be zero, so c \neq 0 and c \neq 3.

Explanation

1. Simplify the equation<br /> Combine fractions on the left side: $\frac{1}{c-3} - \frac{1}{c} = \frac{c - (c-3)}{c(c-3)} = \frac{3}{c(c-3)}$.<br />2. Compare both sides<br /> Both sides are equal: $\frac{3}{c(c-3)} = \frac{3}{c(c-3)}$.<br />3. Identify restrictions<br /> Denominator cannot be zero, so $c \neq 0$ and $c \neq 3$.
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