Evaluate
-\frac{a-1}{\left(a+1\right)\left(2a+1\right)}
Expand
-\frac{a-1}{\left(a+1\right)\left(2a+1\right)}
Quiz
Polynomial
5 problems similar to:
\frac { \frac { a } { a + 1 } - 1 } { \frac { 2 a + 1 } { a - 1 } }
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\frac{\frac{a}{a+1}-\frac{a+1}{a+1}}{\frac{2a+1}{a-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+1}{a+1}.
\frac{\frac{a-\left(a+1\right)}{a+1}}{\frac{2a+1}{a-1}}
Since \frac{a}{a+1} and \frac{a+1}{a+1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{a-a-1}{a+1}}{\frac{2a+1}{a-1}}
Do the multiplications in a-\left(a+1\right).
\frac{\frac{-1}{a+1}}{\frac{2a+1}{a-1}}
Combine like terms in a-a-1.
\frac{-\left(a-1\right)}{\left(a+1\right)\left(2a+1\right)}
Divide \frac{-1}{a+1} by \frac{2a+1}{a-1} by multiplying \frac{-1}{a+1} by the reciprocal of \frac{2a+1}{a-1}.
\frac{-a-\left(-1\right)}{\left(a+1\right)\left(2a+1\right)}
To find the opposite of a-1, find the opposite of each term.
\frac{-a+1}{\left(a+1\right)\left(2a+1\right)}
The opposite of -1 is 1.
\frac{-a+1}{2a^{2}+a+2a+1}
Apply the distributive property by multiplying each term of a+1 by each term of 2a+1.
\frac{-a+1}{2a^{2}+3a+1}
Combine a and 2a to get 3a.
\frac{\frac{a}{a+1}-\frac{a+1}{a+1}}{\frac{2a+1}{a-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+1}{a+1}.
\frac{\frac{a-\left(a+1\right)}{a+1}}{\frac{2a+1}{a-1}}
Since \frac{a}{a+1} and \frac{a+1}{a+1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{a-a-1}{a+1}}{\frac{2a+1}{a-1}}
Do the multiplications in a-\left(a+1\right).
\frac{\frac{-1}{a+1}}{\frac{2a+1}{a-1}}
Combine like terms in a-a-1.
\frac{-\left(a-1\right)}{\left(a+1\right)\left(2a+1\right)}
Divide \frac{-1}{a+1} by \frac{2a+1}{a-1} by multiplying \frac{-1}{a+1} by the reciprocal of \frac{2a+1}{a-1}.
\frac{-a-\left(-1\right)}{\left(a+1\right)\left(2a+1\right)}
To find the opposite of a-1, find the opposite of each term.
\frac{-a+1}{\left(a+1\right)\left(2a+1\right)}
The opposite of -1 is 1.
\frac{-a+1}{2a^{2}+a+2a+1}
Apply the distributive property by multiplying each term of a+1 by each term of 2a+1.
\frac{-a+1}{2a^{2}+3a+1}
Combine a and 2a to get 3a.
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}