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-\frac{1}{r+1}
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-\frac{1}{r+1}
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\left(\frac{3\left(r-2\right)}{\left(r-2\right)\left(r+1\right)}-\frac{4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)}\right)\times \frac{r-2}{r+10}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r+1 and r-2 is \left(r-2\right)\left(r+1\right). Multiply \frac{3}{r+1} times \frac{r-2}{r-2}. Multiply \frac{4}{r-2} times \frac{r+1}{r+1}.
\frac{3\left(r-2\right)-4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Since \frac{3\left(r-2\right)}{\left(r-2\right)\left(r+1\right)} and \frac{4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3r-6-4r-4}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Do the multiplications in 3\left(r-2\right)-4\left(r+1\right).
\frac{-r-10}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Combine like terms in 3r-6-4r-4.
\frac{\left(-r-10\right)\left(r-2\right)}{\left(r-2\right)\left(r+1\right)\left(r+10\right)}
Multiply \frac{-r-10}{\left(r-2\right)\left(r+1\right)} times \frac{r-2}{r+10} by multiplying numerator times numerator and denominator times denominator.
\frac{-\left(r-2\right)\left(r+10\right)}{\left(r-2\right)\left(r+1\right)\left(r+10\right)}
Extract the negative sign in -r-10.
\frac{-1}{r+1}
Cancel out \left(r-2\right)\left(r+10\right) in both numerator and denominator.
\left(\frac{3\left(r-2\right)}{\left(r-2\right)\left(r+1\right)}-\frac{4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)}\right)\times \frac{r-2}{r+10}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r+1 and r-2 is \left(r-2\right)\left(r+1\right). Multiply \frac{3}{r+1} times \frac{r-2}{r-2}. Multiply \frac{4}{r-2} times \frac{r+1}{r+1}.
\frac{3\left(r-2\right)-4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Since \frac{3\left(r-2\right)}{\left(r-2\right)\left(r+1\right)} and \frac{4\left(r+1\right)}{\left(r-2\right)\left(r+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3r-6-4r-4}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Do the multiplications in 3\left(r-2\right)-4\left(r+1\right).
\frac{-r-10}{\left(r-2\right)\left(r+1\right)}\times \frac{r-2}{r+10}
Combine like terms in 3r-6-4r-4.
\frac{\left(-r-10\right)\left(r-2\right)}{\left(r-2\right)\left(r+1\right)\left(r+10\right)}
Multiply \frac{-r-10}{\left(r-2\right)\left(r+1\right)} times \frac{r-2}{r+10} by multiplying numerator times numerator and denominator times denominator.
\frac{-\left(r-2\right)\left(r+10\right)}{\left(r-2\right)\left(r+1\right)\left(r+10\right)}
Extract the negative sign in -r-10.
\frac{-1}{r+1}
Cancel out \left(r-2\right)\left(r+10\right) in both numerator and denominator.
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}