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