Evaluate
-\frac{x+2y}{x+y}
Expand
-\frac{x+2y}{x+y}
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\frac{x-2y}{x+y}-\frac{x-y}{x+y}+\frac{-x-4y}{x+4y}
Factor the expressions that are not already factored in \frac{-x-4y}{x+4y}.
\frac{x-2y}{x+y}-\frac{x-y}{x+y}+\frac{-\left(x+4y\right)}{x+4y}
Extract the negative sign in -x-4y.
\frac{x-2y}{x+y}-\frac{x-y}{x+y}-1
Cancel out x+4y in both numerator and denominator.
\frac{x-2y-\left(x-y\right)}{x+y}-1
Since \frac{x-2y}{x+y} and \frac{x-y}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{x-2y-x+y}{x+y}-1
Do the multiplications in x-2y-\left(x-y\right).
\frac{-y}{x+y}-1
Combine like terms in x-2y-x+y.
\frac{-y}{x+y}-\frac{x+y}{x+y}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+y}{x+y}.
\frac{-y-\left(x+y\right)}{x+y}
Since \frac{-y}{x+y} and \frac{x+y}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{-y-x-y}{x+y}
Do the multiplications in -y-\left(x+y\right).
\frac{-2y-x}{x+y}
Combine like terms in -y-x-y.
\frac{x-2y}{x+y}-\frac{x-y}{x+y}+\frac{-x-4y}{x+4y}
Factor the expressions that are not already factored in \frac{-x-4y}{x+4y}.
\frac{x-2y}{x+y}-\frac{x-y}{x+y}+\frac{-\left(x+4y\right)}{x+4y}
Extract the negative sign in -x-4y.
\frac{x-2y}{x+y}-\frac{x-y}{x+y}-1
Cancel out x+4y in both numerator and denominator.
\frac{x-2y-\left(x-y\right)}{x+y}-1
Since \frac{x-2y}{x+y} and \frac{x-y}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{x-2y-x+y}{x+y}-1
Do the multiplications in x-2y-\left(x-y\right).
\frac{-y}{x+y}-1
Combine like terms in x-2y-x+y.
\frac{-y}{x+y}-\frac{x+y}{x+y}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+y}{x+y}.
\frac{-y-\left(x+y\right)}{x+y}
Since \frac{-y}{x+y} and \frac{x+y}{x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{-y-x-y}{x+y}
Do the multiplications in -y-\left(x+y\right).
\frac{-2y-x}{x+y}
Combine like terms in -y-x-y.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}