Example

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

Question

$$( ) : \frac { x } { x + y } - \frac { x - y } { x }$$

Answer

$$(-x^2+y^2+Si*IM*m*p*l*f*y*x^2)/(x*(x+y))$$

Solution


Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{Simpl\imath fyx}{x+y}-\frac{x-y}{x}\]
Regroup terms.
\[-\frac{x-y}{x}+\frac{Simpl\imath fyx}{x+y}\]
Rewrite the expression with a common denominator.
\[\frac{-(x-y)(x+y)+Simpl\imath fyxx}{x(x+y)}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{-(x-y)(x+y)+Simpl\imath fy{x}^{2}}{x(x+y)}\]
Regroup terms.
\[\frac{-(x-y)(x+y)+Si\imath mplfy{x}^{2}}{x(x+y)}\]
Expand.
\[\frac{-{x}^{2}+{y}^{2}+Si\imath mplfy{x}^{2}}{x(x+y)}\]
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