Evaluate
\frac{2b}{a\left(a-b\right)}
Expand
\frac{2b}{a\left(a-b\right)}
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\left(\frac{b\left(a+b\right)}{\left(a+b\right)\left(a-b\right)}-\frac{b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}\right)\times \frac{b+a}{ab}
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{b}{a-b} times \frac{a+b}{a+b}. Multiply \frac{b}{a+b} times \frac{a-b}{a-b}.
\frac{b\left(a+b\right)-b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Since \frac{b\left(a+b\right)}{\left(a+b\right)\left(a-b\right)} and \frac{b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{ba+b^{2}-ba+b^{2}}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Do the multiplications in b\left(a+b\right)-b\left(a-b\right).
\frac{2b^{2}}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Combine like terms in ba+b^{2}-ba+b^{2}.
\frac{2b^{2}\left(b+a\right)}{\left(a+b\right)\left(a-b\right)ab}
Multiply \frac{2b^{2}}{\left(a+b\right)\left(a-b\right)} times \frac{b+a}{ab} by multiplying numerator times numerator and denominator times denominator.
\frac{2b}{a\left(a-b\right)}
Cancel out b\left(a+b\right) in both numerator and denominator.
\frac{2b}{a^{2}-ab}
Use the distributive property to multiply a by a-b.
\left(\frac{b\left(a+b\right)}{\left(a+b\right)\left(a-b\right)}-\frac{b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}\right)\times \frac{b+a}{ab}
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{b}{a-b} times \frac{a+b}{a+b}. Multiply \frac{b}{a+b} times \frac{a-b}{a-b}.
\frac{b\left(a+b\right)-b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Since \frac{b\left(a+b\right)}{\left(a+b\right)\left(a-b\right)} and \frac{b\left(a-b\right)}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{ba+b^{2}-ba+b^{2}}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Do the multiplications in b\left(a+b\right)-b\left(a-b\right).
\frac{2b^{2}}{\left(a+b\right)\left(a-b\right)}\times \frac{b+a}{ab}
Combine like terms in ba+b^{2}-ba+b^{2}.
\frac{2b^{2}\left(b+a\right)}{\left(a+b\right)\left(a-b\right)ab}
Multiply \frac{2b^{2}}{\left(a+b\right)\left(a-b\right)} times \frac{b+a}{ab} by multiplying numerator times numerator and denominator times denominator.
\frac{2b}{a\left(a-b\right)}
Cancel out b\left(a+b\right) in both numerator and denominator.
\frac{2b}{a^{2}-ab}
Use the distributive property to multiply a by a-b.
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}