Solve and check
(c-4/c-2)=(c-2/c+2)-(1/2-c)
WHAT IS THE SOLUTION AND HOW MANY EXTRANEOUS SOLUTIONS ARE THERE?

Question

shamim · Answer

c-4/c-2=c-2/c+2-1/2-c
c-4/c+2/c=2-1/2+2

tkhunny · Answer

Are c and C the same thing?

c-4/c-2 = $c - \dfrac{4}{c} - 2$  Is that what you intended?

Use parentheses to clarify intent.

mathmale · Answer

For starters, would you please consider re-writing your equation in a form less likely to be misinterpreted?    either use parentheses to the order of operations you intend.  A more sophisticated approach would be to Use either Equation Editor or Draw to present your math problem.

why force your potential helpers to guess what you mean?

mathmale · Answer

$$c-4/c-2=C-2/C+2-1/2-C$$

mathmale · Answer

...possibly was meant to mean $$\frac{ c-4 }{ c-2 }$$...~etc.

anonymous · Answer

attachment

anonymous · Answer

just commented my question in picture form

tkhunny · Answer

For starters, the only POSSIBLE extraneous solutions are 2 and -2.  You shoudl see this from the denominators.

tkhunny · Answer

The picture is nice, but you should also spend some pondering why what you wrote does not mean what it says in the picture.

anonymous · Answer

im sorry im a started so i didnt know how o draw my question in just please help me find "c"

tkhunny · Answer

It's not a matter of "sorry".  It's a matter of you learning to communicate.  That's all.  Order of Operations is important.

Generally, how would you add three fractions?

anonymous · Answer

$$\frac{ c-4 }{c-2}= \frac{ c-2}{ c+2}-\frac{ 1 }{ 2-c }$$

tkhunny · Answer

Okay, now answer my question.

mathmale · Answer

Here you have 3 different denominators.  How does one combine fractions that have different denominators?  

How would one combine the following?$$\frac{ 1 }{ 7 },\frac{ 1 }{ 6 }?$$

anonymous · Answer

LCD

mathmale · Answer

Right.  And precisely the same principle applies to your equation$$\frac{ c-4 }{c-2}= \frac{ c-2}{ c+2}-\frac{ 1 }{ 2-c }$$

mathmale · Answer

You'll need to identify the LCD and then use it to eliminate all the denominators.  Where would you start here?

Hint:  You could save yourself some work by recognizing that the denominator (2-c) is the same as -(c-2).

anonymous · Answer

and the negative 1 would change the subtraction sign into to an addition sign right?

anonymous · Answer

but how would i get the $$\frac{ c-2 }{ c+2}$$ to have the denominator of c-2 like the rest?

mathmale · Answer

Please go back to my example:$$\frac{ 1 }{ 7 }+\frac{ 1 }{ 6 }$$what is the LCD?  How would you obtain the same denominator in both fractions so as to be able to add the two fractions together?  I'm sure you've done this before.

mathmale · Answer

Hint:  Multiply 7 and 6 together.  Why?  What is the LCD in this example?