Which expression is equivalent to the following complex fraction?

mc019-1.jpg

Question

Which expression is equivalent to the following complex fraction?

mc019-1.jpg

anonymous · Answer

$$1+\frac{ 1 }{ y }\div 1- \frac{ 1 }{ y }$$

anonymous · Answer

@Mathhelp123344

anonymous · Answer

@mathmale

anonymous · Answer

@IMstuck

anonymous · Answer

@cwrw238

mathmale · Answer

$$1+\frac{ 1 }{ y }\div 1- \frac{ 1 }{ y }$$...if interpreted exactly as you have typed it, would require dividing (1/y) by 1, because we MUST perform multiplication and division BEFORE addition and subtraction.  Dividing (1/y) by 1 doesn't make much sense, does it?

I suspect that what you actually have here is$$\frac{ 1+\frac{ 1 }{ y } }{ 1-\frac{ 1 }{ y } },$$

mathmale · Answer

.../which could also be expressed, using parentheses liberally, as (1 + 1/y) / (1 - 1/y).

In any case, if your readers have to figure out your possible meanings, valuable time will be lost.  

So I'm asking you to go back to the original problem and to type it again here, using parentheses or Equation Editor, in such a way that leaves no doubt regarding your meaning.  Then we can discuss how to solve the problem.

anonymous · Answer

What is the quotient of $$\frac{ 2^{4} }{ 2^{-4}}$$

anonymous · Answer

@mathmale

anonymous · Answer

would the answer be 256

mathmale · Answer

Would you mind showing or explaining how you obtained that '256'?

mathmale · Answer

Hint:$$\frac{ 2^a }{ 2^b }=2^{a-b}$$

anonymous · Answer

2^4 = 16
2^-4 =.0625 
and i just divided both those answers

anonymous · Answer

OHhhhhh ok ive been doing this wrong all along

anonymous · Answer

so the answer would be 1

mathmale · Answer

that works fine and is legitimate.  If you use the example I gave you (above), you'll get$$\frac{ 2^4 }{ 2^{-4} }=2^{4-(-4)}=2^8=??$$

mathmale · Answer

No, it's not 1.  Try finishing the calculation above.  what is 2^8?

anonymous · Answer

so 256

mathmale · Answer

Right.  2^8 = 256.  2^8 also equals (2^4)^2=16^2 = 256.  You OK with this?

anonymous · Answer

Which value is equivalent to  $$\frac{ x+4 }{ 4+x }$$?
–4
–1
1
4

anonymous · Answer

yes i am

anonymous · Answer

@mathmale

mathmale · Answer

Regarding:$$\frac{ x+4 }{ 4+x }$$...I'd prefer you post each new question in the "Ask a question" box.

But anyway, ...$$\frac{ x+4 }{ 4+x }$$ can be re-written as $$\frac{ x+4 }{ x+4 }$$...without changing its value.  Please reduce this.

anonymous · Answer

wouldnt it just be 1