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