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\frac{b}{2\left(3b-2a\right)}
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\frac{b}{2\left(3b-2a\right)}
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\frac{\frac{2ab}{\left(2a-3b\right)\left(2a+3b\right)}+\frac{b}{3b-2a}}{1-\frac{2a-3b}{2a+3b}}
Factor 4a^{2}-9b^{2}.
\frac{\frac{-2ab}{\left(-2a-3b\right)\left(2a-3b\right)}+\frac{b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2a-3b\right)\left(2a+3b\right) and 3b-2a is \left(-2a-3b\right)\left(2a-3b\right). Multiply \frac{2ab}{\left(2a-3b\right)\left(2a+3b\right)} times \frac{-1}{-1}. Multiply \frac{b}{3b-2a} times \frac{-\left(-2a-3b\right)}{-\left(-2a-3b\right)}.
\frac{\frac{-2ab+b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Since \frac{-2ab}{\left(-2a-3b\right)\left(2a-3b\right)} and \frac{b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{-2ab+2ba+3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Do the multiplications in -2ab+b\left(-1\right)\left(-2a-3b\right).
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Combine like terms in -2ab+2ba+3b^{2}.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b}{2a+3b}-\frac{2a-3b}{2a+3b}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2a+3b}{2a+3b}.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b-\left(2a-3b\right)}{2a+3b}}
Since \frac{2a+3b}{2a+3b} and \frac{2a-3b}{2a+3b} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b-2a+3b}{2a+3b}}
Do the multiplications in 2a+3b-\left(2a-3b\right).
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{6b}{2a+3b}}
Combine like terms in 2a+3b-2a+3b.
\frac{3b^{2}\left(2a+3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)\times 6b}
Divide \frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)} by \frac{6b}{2a+3b} by multiplying \frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)} by the reciprocal of \frac{6b}{2a+3b}.
\frac{-3\left(-2a-3b\right)b^{2}}{6b\left(-2a-3b\right)\left(2a-3b\right)}
Extract the negative sign in 2a+3b.
\frac{-b}{2\left(2a-3b\right)}
Cancel out 3b\left(-2a-3b\right) in both numerator and denominator.
\frac{b}{-2\left(2a-3b\right)}
Cancel out -1 in both numerator and denominator.
\frac{b}{-4a+6b}
Use the distributive property to multiply -2 by 2a-3b.
\frac{\frac{2ab}{\left(2a-3b\right)\left(2a+3b\right)}+\frac{b}{3b-2a}}{1-\frac{2a-3b}{2a+3b}}
Factor 4a^{2}-9b^{2}.
\frac{\frac{-2ab}{\left(-2a-3b\right)\left(2a-3b\right)}+\frac{b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2a-3b\right)\left(2a+3b\right) and 3b-2a is \left(-2a-3b\right)\left(2a-3b\right). Multiply \frac{2ab}{\left(2a-3b\right)\left(2a+3b\right)} times \frac{-1}{-1}. Multiply \frac{b}{3b-2a} times \frac{-\left(-2a-3b\right)}{-\left(-2a-3b\right)}.
\frac{\frac{-2ab+b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Since \frac{-2ab}{\left(-2a-3b\right)\left(2a-3b\right)} and \frac{b\left(-1\right)\left(-2a-3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{-2ab+2ba+3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Do the multiplications in -2ab+b\left(-1\right)\left(-2a-3b\right).
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{1-\frac{2a-3b}{2a+3b}}
Combine like terms in -2ab+2ba+3b^{2}.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b}{2a+3b}-\frac{2a-3b}{2a+3b}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2a+3b}{2a+3b}.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b-\left(2a-3b\right)}{2a+3b}}
Since \frac{2a+3b}{2a+3b} and \frac{2a-3b}{2a+3b} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{2a+3b-2a+3b}{2a+3b}}
Do the multiplications in 2a+3b-\left(2a-3b\right).
\frac{\frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)}}{\frac{6b}{2a+3b}}
Combine like terms in 2a+3b-2a+3b.
\frac{3b^{2}\left(2a+3b\right)}{\left(-2a-3b\right)\left(2a-3b\right)\times 6b}
Divide \frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)} by \frac{6b}{2a+3b} by multiplying \frac{3b^{2}}{\left(-2a-3b\right)\left(2a-3b\right)} by the reciprocal of \frac{6b}{2a+3b}.
\frac{-3\left(-2a-3b\right)b^{2}}{6b\left(-2a-3b\right)\left(2a-3b\right)}
Extract the negative sign in 2a+3b.
\frac{-b}{2\left(2a-3b\right)}
Cancel out 3b\left(-2a-3b\right) in both numerator and denominator.
\frac{b}{-2\left(2a-3b\right)}
Cancel out -1 in both numerator and denominator.
\frac{b}{-4a+6b}
Use the distributive property to multiply -2 by 2a-3b.
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}