Evaluate
-\frac{w+2}{2w+1}
Expand
-\frac{w+2}{2w+1}
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\frac{\left(w+2\right)\left(w+7\right)}{2^{2}w^{2}-1^{2}}\times \frac{1-2w}{w+7}
Expand \left(2w\right)^{2}.
\frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1^{2}}\times \frac{1-2w}{w+7}
Calculate 2 to the power of 2 and get 4.
\frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1}\times \frac{1-2w}{w+7}
Calculate 1 to the power of 2 and get 1.
\frac{\left(w+2\right)\left(w+7\right)\left(1-2w\right)}{\left(4w^{2}-1\right)\left(w+7\right)}
Multiply \frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1} times \frac{1-2w}{w+7} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(w+2\right)\left(-2w+1\right)}{4w^{2}-1}
Cancel out w+7 in both numerator and denominator.
\frac{\left(w+2\right)\left(-2w+1\right)}{\left(2w-1\right)\left(2w+1\right)}
Factor the expressions that are not already factored.
\frac{-\left(2w-1\right)\left(w+2\right)}{\left(2w-1\right)\left(2w+1\right)}
Extract the negative sign in 1-2w.
\frac{-\left(w+2\right)}{2w+1}
Cancel out 2w-1 in both numerator and denominator.
\frac{-w-2}{2w+1}
Expand the expression.
\frac{\left(w+2\right)\left(w+7\right)}{2^{2}w^{2}-1^{2}}\times \frac{1-2w}{w+7}
Expand \left(2w\right)^{2}.
\frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1^{2}}\times \frac{1-2w}{w+7}
Calculate 2 to the power of 2 and get 4.
\frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1}\times \frac{1-2w}{w+7}
Calculate 1 to the power of 2 and get 1.
\frac{\left(w+2\right)\left(w+7\right)\left(1-2w\right)}{\left(4w^{2}-1\right)\left(w+7\right)}
Multiply \frac{\left(w+2\right)\left(w+7\right)}{4w^{2}-1} times \frac{1-2w}{w+7} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(w+2\right)\left(-2w+1\right)}{4w^{2}-1}
Cancel out w+7 in both numerator and denominator.
\frac{\left(w+2\right)\left(-2w+1\right)}{\left(2w-1\right)\left(2w+1\right)}
Factor the expressions that are not already factored.
\frac{-\left(2w-1\right)\left(w+2\right)}{\left(2w-1\right)\left(2w+1\right)}
Extract the negative sign in 1-2w.
\frac{-\left(w+2\right)}{2w+1}
Cancel out 2w-1 in both numerator and denominator.
\frac{-w-2}{2w+1}
Expand the expression.
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}