Question

$$\frac{ 2(x+1) }{ xy } - \frac{ 3(2-y) }{ 3y }$$

Answer

1+2/(x*y)

Solution


Cancel \(3\).
\[\frac{2(x+1)}{xy}-\frac{2-y}{y}\]
Rewrite the expression with a common denominator.
\[\frac{2(x+1)-(2-y)x}{xy}\]
Regroup terms.
\[\frac{2(x+1)-x(2-y)}{xy}\]
Expand.
\[\frac{2x+2-2x+xy}{xy}\]
Collect like terms.
\[\frac{(2x-2x)+2+xy}{xy}\]
Simplify  \((2x-2x)+2+xy\)  to  \(2+xy\).
\[\frac{2+xy}{xy}\]
Simplify.
\[1+\frac{2}{xy}\]