Evaluate
\frac{\left(2a+b\right)\left(3a+b\right)}{3\left(a+2b\right)}
Expand
\frac{6a^{2}+5ab+b^{2}}{3\left(a+2b\right)}
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\frac{\left(b+2a\right)\left(b+3a\right)}{3\left(2b+a\right)}
Multiply \frac{b+2a}{3} times \frac{b+3a}{2b+a} by multiplying numerator times numerator and denominator times denominator.
\frac{b^{2}+3ba+2ab+6a^{2}}{3\left(2b+a\right)}
Apply the distributive property by multiplying each term of b+2a by each term of b+3a.
\frac{b^{2}+5ba+6a^{2}}{3\left(2b+a\right)}
Combine 3ba and 2ab to get 5ba.
\frac{b^{2}+5ba+6a^{2}}{6b+3a}
Use the distributive property to multiply 3 by 2b+a.
\frac{\left(b+2a\right)\left(b+3a\right)}{3\left(2b+a\right)}
Multiply \frac{b+2a}{3} times \frac{b+3a}{2b+a} by multiplying numerator times numerator and denominator times denominator.
\frac{b^{2}+3ba+2ab+6a^{2}}{3\left(2b+a\right)}
Apply the distributive property by multiplying each term of b+2a by each term of b+3a.
\frac{b^{2}+5ba+6a^{2}}{3\left(2b+a\right)}
Combine 3ba and 2ab to get 5ba.
\frac{b^{2}+5ba+6a^{2}}{6b+3a}
Use the distributive property to multiply 3 by 2b+a.
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}