Question

Simplify the fraction. Fraction is included in attachment.

Answer 1

we need to get both upper and lower fractions the same denominator, which will be x*y.
then we have to multiply 1 with x in the first upper fraction and 1 with y.
we apply the same procedure on the lower fractions, again the common denominator will be x*y
\[\frac{ \frac{ 1 }{ y }+\frac{ 1 }{ x } }{ \frac{ 1 }{ y } - \frac{ 1 }{ x } } = \frac{ \frac{ x + y }{ yx } }{ \frac{ x-y }{ yx } } = ...\]

can you finish from here?
if you have any more question, feel free to ask;)

Answer 2

Alternatively you can approach it another way that may be more intuitive for you.

\[\frac{\frac{1}{y} + \frac{1}{x}}{\frac{1}{y} - \frac{1}{x}}=\left(\frac{1}{y} + \frac{1}{x}\right) \div \left(\frac{1}{y} - \frac{1}{x}\right) = \left(\frac{x + y}{yx} \right) \times \left(\frac{yx}{x-y}\right)\]

Answer 3

Perhaps you could finish simplifying it if you understand it.

Answer 4

Hint: There's something that "cancels" in the final simplification.

Answer 5

\[\frac{ x+y }{ x-y }\]

Answer 6

yes indeed;)

Answer 7

Yes, very good use of the latex. The question, however, is whether or not you understood the intermediary steps.

Answer 8

I've used similar steps with other problems, the 1s were just throwing me off.

Answer 9

For the fractions with the '1s', you multiply the first fraction by x/x. Then multiply the second fraction by y/y.

Answer 10

Got it. :)