Evaluate
-\frac{a}{a^{2}+a+1}
Expand
-\frac{a}{a^{2}+a+1}
Quiz
Polynomial
5 problems similar to:
1 + \frac { 2 a + 1 } { a ^ { 3 } - 1 } - \frac { a } { a - 1 }
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1+\frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Factor a^{3}-1.
\frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}+\frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}.
\frac{\left(a-1\right)\left(a^{2}+a+1\right)+2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Since \frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)} and \frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)} have the same denominator, add them by adding their numerators.
\frac{a^{3}+a^{2}+a-a^{2}-a-1+2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Do the multiplications in \left(a-1\right)\left(a^{2}+a+1\right)+2a+1.
\frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Combine like terms in a^{3}+a^{2}+a-a^{2}-a-1+2a+1.
\frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-1\right)\left(a^{2}+a+1\right) and a-1 is \left(a-1\right)\left(a^{2}+a+1\right). Multiply \frac{a}{a-1} times \frac{a^{2}+a+1}{a^{2}+a+1}.
\frac{a^{3}+2a-a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Since \frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)} and \frac{a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{3}+2a-a^{3}-a^{2}-a}{\left(a-1\right)\left(a^{2}+a+1\right)}
Do the multiplications in a^{3}+2a-a\left(a^{2}+a+1\right).
\frac{a-a^{2}}{\left(a-1\right)\left(a^{2}+a+1\right)}
Combine like terms in a^{3}+2a-a^{3}-a^{2}-a.
\frac{a\left(-a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Factor the expressions that are not already factored in \frac{a-a^{2}}{\left(a-1\right)\left(a^{2}+a+1\right)}.
\frac{-a\left(a-1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Extract the negative sign in 1-a.
\frac{-a}{a^{2}+a+1}
Cancel out a-1 in both numerator and denominator.
1+\frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Factor a^{3}-1.
\frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}+\frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}.
\frac{\left(a-1\right)\left(a^{2}+a+1\right)+2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Since \frac{\left(a-1\right)\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)} and \frac{2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)} have the same denominator, add them by adding their numerators.
\frac{a^{3}+a^{2}+a-a^{2}-a-1+2a+1}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Do the multiplications in \left(a-1\right)\left(a^{2}+a+1\right)+2a+1.
\frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a}{a-1}
Combine like terms in a^{3}+a^{2}+a-a^{2}-a-1+2a+1.
\frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)}-\frac{a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-1\right)\left(a^{2}+a+1\right) and a-1 is \left(a-1\right)\left(a^{2}+a+1\right). Multiply \frac{a}{a-1} times \frac{a^{2}+a+1}{a^{2}+a+1}.
\frac{a^{3}+2a-a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Since \frac{a^{3}+2a}{\left(a-1\right)\left(a^{2}+a+1\right)} and \frac{a\left(a^{2}+a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a^{3}+2a-a^{3}-a^{2}-a}{\left(a-1\right)\left(a^{2}+a+1\right)}
Do the multiplications in a^{3}+2a-a\left(a^{2}+a+1\right).
\frac{a-a^{2}}{\left(a-1\right)\left(a^{2}+a+1\right)}
Combine like terms in a^{3}+2a-a^{3}-a^{2}-a.
\frac{a\left(-a+1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Factor the expressions that are not already factored in \frac{a-a^{2}}{\left(a-1\right)\left(a^{2}+a+1\right)}.
\frac{-a\left(a-1\right)}{\left(a-1\right)\left(a^{2}+a+1\right)}
Extract the negative sign in 1-a.
\frac{-a}{a^{2}+a+1}
Cancel out a-1 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}