Evaluate
-\frac{1}{3\left(x+1\right)}
Expand
-\frac{1}{3\left(x+1\right)}
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\left(\frac{x+1}{3\left(x-1\right)}-\frac{4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Factor 3x-3. Factor 3x^{2}-3.
\left(\frac{\left(x+1\right)\left(x+1\right)}{3\left(x-1\right)\left(x+1\right)}-\frac{4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-1\right) and 3\left(x-1\right)\left(x+1\right) is 3\left(x-1\right)\left(x+1\right). Multiply \frac{x+1}{3\left(x-1\right)} times \frac{x+1}{x+1}.
\left(\frac{\left(x+1\right)\left(x+1\right)-4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Since \frac{\left(x+1\right)\left(x+1\right)}{3\left(x-1\right)\left(x+1\right)} and \frac{4}{3\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\left(\frac{x^{2}+x+x+1-4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Do the multiplications in \left(x+1\right)\left(x+1\right)-4.
\left(\frac{x^{2}+2x-3}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Combine like terms in x^{2}+x+x+1-4.
\left(\frac{\left(x-1\right)\left(x+3\right)}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Factor the expressions that are not already factored in \frac{x^{2}+2x-3}{3\left(x-1\right)\left(x+1\right)}.
\left(\frac{x+3}{3\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Cancel out x-1 in both numerator and denominator.
\left(\frac{x+3}{3\left(x+1\right)}-\frac{x+10}{3\left(x+1\right)}\right)\times \frac{1}{7}
Factor 3x+3.
\frac{x+3-\left(x+10\right)}{3\left(x+1\right)}\times \frac{1}{7}
Since \frac{x+3}{3\left(x+1\right)} and \frac{x+10}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-x-10}{3\left(x+1\right)}\times \frac{1}{7}
Do the multiplications in x+3-\left(x+10\right).
\frac{-7}{3\left(x+1\right)}\times \frac{1}{7}
Combine like terms in x+3-x-10.
\frac{-7}{3\left(x+1\right)\times 7}
Multiply \frac{-7}{3\left(x+1\right)} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.
\frac{-7}{21\left(x+1\right)}
Multiply 3 and 7 to get 21.
\frac{-7}{21x+21}
Use the distributive property to multiply 21 by x+1.
\left(\frac{x+1}{3\left(x-1\right)}-\frac{4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Factor 3x-3. Factor 3x^{2}-3.
\left(\frac{\left(x+1\right)\left(x+1\right)}{3\left(x-1\right)\left(x+1\right)}-\frac{4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-1\right) and 3\left(x-1\right)\left(x+1\right) is 3\left(x-1\right)\left(x+1\right). Multiply \frac{x+1}{3\left(x-1\right)} times \frac{x+1}{x+1}.
\left(\frac{\left(x+1\right)\left(x+1\right)-4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Since \frac{\left(x+1\right)\left(x+1\right)}{3\left(x-1\right)\left(x+1\right)} and \frac{4}{3\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\left(\frac{x^{2}+x+x+1-4}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Do the multiplications in \left(x+1\right)\left(x+1\right)-4.
\left(\frac{x^{2}+2x-3}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Combine like terms in x^{2}+x+x+1-4.
\left(\frac{\left(x-1\right)\left(x+3\right)}{3\left(x-1\right)\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Factor the expressions that are not already factored in \frac{x^{2}+2x-3}{3\left(x-1\right)\left(x+1\right)}.
\left(\frac{x+3}{3\left(x+1\right)}-\frac{x+10}{3x+3}\right)\times \frac{1}{7}
Cancel out x-1 in both numerator and denominator.
\left(\frac{x+3}{3\left(x+1\right)}-\frac{x+10}{3\left(x+1\right)}\right)\times \frac{1}{7}
Factor 3x+3.
\frac{x+3-\left(x+10\right)}{3\left(x+1\right)}\times \frac{1}{7}
Since \frac{x+3}{3\left(x+1\right)} and \frac{x+10}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-x-10}{3\left(x+1\right)}\times \frac{1}{7}
Do the multiplications in x+3-\left(x+10\right).
\frac{-7}{3\left(x+1\right)}\times \frac{1}{7}
Combine like terms in x+3-x-10.
\frac{-7}{3\left(x+1\right)\times 7}
Multiply \frac{-7}{3\left(x+1\right)} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.
\frac{-7}{21\left(x+1\right)}
Multiply 3 and 7 to get 21.
\frac{-7}{21x+21}
Use the distributive property to multiply 21 by x+1.
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}