Evaluate
\frac{\left(a+4\right)\left(2a+b\right)}{a+3}
Expand
\frac{2a^{2}+ab+8a+4b}{a+3}
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\frac{\frac{\left(a-3\right)\left(a+3\right)}{a+3}-\frac{7}{a+3}}{\frac{a-4}{2a+b}}
To add or subtract expressions, expand them to make their denominators the same. Multiply a-3 times \frac{a+3}{a+3}.
\frac{\frac{\left(a-3\right)\left(a+3\right)-7}{a+3}}{\frac{a-4}{2a+b}}
Since \frac{\left(a-3\right)\left(a+3\right)}{a+3} and \frac{7}{a+3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{a^{2}+3a-3a-9-7}{a+3}}{\frac{a-4}{2a+b}}
Do the multiplications in \left(a-3\right)\left(a+3\right)-7.
\frac{\frac{a^{2}-16}{a+3}}{\frac{a-4}{2a+b}}
Combine like terms in a^{2}+3a-3a-9-7.
\frac{\left(a^{2}-16\right)\left(2a+b\right)}{\left(a+3\right)\left(a-4\right)}
Divide \frac{a^{2}-16}{a+3} by \frac{a-4}{2a+b} by multiplying \frac{a^{2}-16}{a+3} by the reciprocal of \frac{a-4}{2a+b}.
\frac{\left(a-4\right)\left(a+4\right)\left(2a+b\right)}{\left(a-4\right)\left(a+3\right)}
Factor the expressions that are not already factored.
\frac{\left(a+4\right)\left(2a+b\right)}{a+3}
Cancel out a-4 in both numerator and denominator.
\frac{2a^{2}+ab+8a+4b}{a+3}
Expand the expression.
\frac{\frac{\left(a-3\right)\left(a+3\right)}{a+3}-\frac{7}{a+3}}{\frac{a-4}{2a+b}}
To add or subtract expressions, expand them to make their denominators the same. Multiply a-3 times \frac{a+3}{a+3}.
\frac{\frac{\left(a-3\right)\left(a+3\right)-7}{a+3}}{\frac{a-4}{2a+b}}
Since \frac{\left(a-3\right)\left(a+3\right)}{a+3} and \frac{7}{a+3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{a^{2}+3a-3a-9-7}{a+3}}{\frac{a-4}{2a+b}}
Do the multiplications in \left(a-3\right)\left(a+3\right)-7.
\frac{\frac{a^{2}-16}{a+3}}{\frac{a-4}{2a+b}}
Combine like terms in a^{2}+3a-3a-9-7.
\frac{\left(a^{2}-16\right)\left(2a+b\right)}{\left(a+3\right)\left(a-4\right)}
Divide \frac{a^{2}-16}{a+3} by \frac{a-4}{2a+b} by multiplying \frac{a^{2}-16}{a+3} by the reciprocal of \frac{a-4}{2a+b}.
\frac{\left(a-4\right)\left(a+4\right)\left(2a+b\right)}{\left(a-4\right)\left(a+3\right)}
Factor the expressions that are not already factored.
\frac{\left(a+4\right)\left(2a+b\right)}{a+3}
Cancel out a-4 in both numerator and denominator.
\frac{2a^{2}+ab+8a+4b}{a+3}
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}