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