Evaluate
\frac{2\left(\left(a-2\right)^{2}-9b^{2}\right)}{3b\left(a-2\right)}
Expand
-\frac{2\left(-a^{2}+4a+9b^{2}-4\right)}{3b\left(a-2\right)}
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\frac{\left(2a-4\right)\left(a-2\right)}{3b\left(a-2\right)}-\frac{6b\times 3b}{3b\left(a-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3b and a-2 is 3b\left(a-2\right). Multiply \frac{2a-4}{3b} times \frac{a-2}{a-2}. Multiply \frac{6b}{a-2} times \frac{3b}{3b}.
\frac{\left(2a-4\right)\left(a-2\right)-6b\times 3b}{3b\left(a-2\right)}
Since \frac{\left(2a-4\right)\left(a-2\right)}{3b\left(a-2\right)} and \frac{6b\times 3b}{3b\left(a-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2a^{2}-4a-4a+8-18b^{2}}{3b\left(a-2\right)}
Do the multiplications in \left(2a-4\right)\left(a-2\right)-6b\times 3b.
\frac{2a^{2}-8a+8-18b^{2}}{3b\left(a-2\right)}
Combine like terms in 2a^{2}-4a-4a+8-18b^{2}.
\frac{2a^{2}-8a+8-18b^{2}}{3ab-6b}
Expand 3b\left(a-2\right).
\frac{\left(2a-4\right)\left(a-2\right)}{3b\left(a-2\right)}-\frac{6b\times 3b}{3b\left(a-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3b and a-2 is 3b\left(a-2\right). Multiply \frac{2a-4}{3b} times \frac{a-2}{a-2}. Multiply \frac{6b}{a-2} times \frac{3b}{3b}.
\frac{\left(2a-4\right)\left(a-2\right)-6b\times 3b}{3b\left(a-2\right)}
Since \frac{\left(2a-4\right)\left(a-2\right)}{3b\left(a-2\right)} and \frac{6b\times 3b}{3b\left(a-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2a^{2}-4a-4a+8-18b^{2}}{3b\left(a-2\right)}
Do the multiplications in \left(2a-4\right)\left(a-2\right)-6b\times 3b.
\frac{2a^{2}-8a+8-18b^{2}}{3b\left(a-2\right)}
Combine like terms in 2a^{2}-4a-4a+8-18b^{2}.
\frac{2a^{2}-8a+8-18b^{2}}{3ab-6b}
Expand 3b\left(a-2\right).
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}