Im not sure if this is right so I'm making sure.

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The discussion revolves around solving the equation $$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{\frac{5}{6}}{\frac{x}{8}}$$ for the variable x. Participants clarify that the original expression must be treated as an equation to find x, emphasizing the need for complete information. A method to simplify the equation is suggested, involving multiplying both sides to eliminate fractions. The final goal is to determine that x equals 32, based on the provided context. The conversation highlights challenges in sharing mathematical workings online, particularly with LaTeX formatting.
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Homework Statement


Revised by mentor:
Solve for x
$$\frac{\frac 1 2}{\frac 3 4 } = \frac{\frac 5 6 }{\frac x 8 } $$

Note to OP: This is $$\frac{\frac 1 2}{\frac 3 4 } = \frac{\frac 5 6 }{\frac x 8 } $$

Homework Equations


$$\frac{\frac{a}{x}}{\frac{c}{1}}$$

The Attempt at a Solution


I don't know how to post my workings but here's the answer I got
X= $$\frac{BCD}{E}$$
 
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Joshper14 said:

Homework Statement


Solving for x

$$\frac{\frac{x}{b}}{\frac{c}{1}}$$
This isn't an equation, so you can't "solve for x".
Are you given some information about what the expression above is equal to? If so, that's an equation, so you can solve for x or one of the other variables.
Joshper14 said:

Homework Equations


$$\frac{\frac{a}{x}}{\frac{c}{1}}$$

The Attempt at a Solution


I don't know how to post my workings but here's the answer I got
X= $$\frac{BCD}{E}$$
In your original expression there are only the variables x, b, and c. Where did D and E come from?
 
Oh. I'm sorry you see too put what I have on paper onto this site is a pain so and remember that LaTeX code that mixed me up and forgot to put the entire 'question' up I'll upload a picture instead

The only instructions given to me from my teacher was find x. So I was tellin you I'm solving for x but you didn't understand

By the way what we are trying to find is 32
 

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To simplify both sides of this equation ##\frac {\frac A B }{\frac C D} = \frac {\frac E F}{\frac G H}##,
multiply both sides by ##\frac C D \cdot \frac G H##. That will "cancel" the fractions in the denominators, simplifying the equation above to ##\frac A B \cdot \frac G H = \frac E F \cdot \frac C D##. At this stage you can get rid of common factors ("cancel") on each side of the equation.
 
Joshper14 said:
Oh. I'm sorry you see too put what I have on paper onto this site is a pain so and remember that LaTeX code that mixed me up and forgot to put the entire 'question' up I'll upload a picture instead

The only instructions given to me from my teacher was find x. So I was telling you I'm solving for x but you didn't understand

By the way what we are trying to find is 32

Here is a snippet of that image you attached.
upload_2016-10-9_19-31-14.png
 
The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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