Prove algebraically that 2/x-3 +2 is equal to 2x-4/x-3

Question

mathmale · Answer

For clarity, it is important that you enclose any denominators in parentheses:

2 / (x-3), NOT 2 / x-3, and -4 / (x-3), not -4 / x-3.

To answer this question, combine the 2 terms on the left side and combine the 2 terms on the right side.  Then compare your results.

dayakar · Answer

$$\frac{ 2 }{ x-3 }+2 =\frac{ 2 }{ x-3}+ \frac{ 2(x-3) }{ (x-3) }$$  [ since x-3/x-3 =1]

can u simplify it

mathmale · Answer

Yes, good suggestion.  Simplify the right side of the equation$$\frac{ 2 }{ x-3 }+2 =\frac{ 2 }{ x-3}+ \frac{ 2(x-3) }{ (x-3) }$$

baby456 · Answer

OK but my teacher means to prove they are the same thing

baby456 · Answer

Like they should equal each other

baby456 · Answer

@mathmale and @dayakar

dayakar · Answer

if u simplify above expression u can get the equal one

mathmale · Answer

I understand what your teacher is asking you to do.  My point is that there is ambiguity in the way you have entered this equation, and I'm asking you to address (fix) that ambiguity.