Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ \frac{ 2xy }{ x+y } -x }{ \frac{ 1 }{ y } + \frac{ 1 }{ x-2y } }$$

Answer

x*((2*y)/(x+y)-1)*(y*(x-2*y))/(x-y)

Solution


Factor out the common term \(x\).
\[\frac{x(\frac{2y}{x+y}-1)}{\frac{1}{y}+\frac{1}{x-2y}}\]
Rewrite the expression with a common denominator.
\[\frac{x(\frac{2y}{x+y}-1)}{\frac{x-2y+y}{y(x-2y)}}\]
Collect like terms.
\[\frac{x(\frac{2y}{x+y}-1)}{\frac{x+(-2y+y)}{y(x-2y)}}\]
Simplify  \(x+(-2y+y)\)  to  \(x-y\).
\[\frac{x(\frac{2y}{x+y}-1)}{\frac{x-y}{y(x-2y)}}\]
Invert and multiply.
\[x(\frac{2y}{x+y}-1)\times \frac{y(x-2y)}{x-y}\]
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