Evaluate
\frac{\left(a+4\right)\left(2a+1\right)}{4a\left(a+2\right)}
Expand
\frac{2a^{2}+9a+4}{4a\left(a+2\right)}
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\frac{a+1}{2a}+\frac{3}{4\left(a+2\right)}
Factor 4a+8.
\frac{\left(a+1\right)\times 2\left(a+2\right)}{4a\left(a+2\right)}+\frac{3a}{4a\left(a+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 4\left(a+2\right) is 4a\left(a+2\right). Multiply \frac{a+1}{2a} times \frac{2\left(a+2\right)}{2\left(a+2\right)}. Multiply \frac{3}{4\left(a+2\right)} times \frac{a}{a}.
\frac{\left(a+1\right)\times 2\left(a+2\right)+3a}{4a\left(a+2\right)}
Since \frac{\left(a+1\right)\times 2\left(a+2\right)}{4a\left(a+2\right)} and \frac{3a}{4a\left(a+2\right)} have the same denominator, add them by adding their numerators.
\frac{2a^{2}+4a+2a+4+3a}{4a\left(a+2\right)}
Do the multiplications in \left(a+1\right)\times 2\left(a+2\right)+3a.
\frac{2a^{2}+9a+4}{4a\left(a+2\right)}
Combine like terms in 2a^{2}+4a+2a+4+3a.
\frac{2a^{2}+9a+4}{4a^{2}+8a}
Expand 4a\left(a+2\right).
\frac{a+1}{2a}+\frac{3}{4\left(a+2\right)}
Factor 4a+8.
\frac{\left(a+1\right)\times 2\left(a+2\right)}{4a\left(a+2\right)}+\frac{3a}{4a\left(a+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 4\left(a+2\right) is 4a\left(a+2\right). Multiply \frac{a+1}{2a} times \frac{2\left(a+2\right)}{2\left(a+2\right)}. Multiply \frac{3}{4\left(a+2\right)} times \frac{a}{a}.
\frac{\left(a+1\right)\times 2\left(a+2\right)+3a}{4a\left(a+2\right)}
Since \frac{\left(a+1\right)\times 2\left(a+2\right)}{4a\left(a+2\right)} and \frac{3a}{4a\left(a+2\right)} have the same denominator, add them by adding their numerators.
\frac{2a^{2}+4a+2a+4+3a}{4a\left(a+2\right)}
Do the multiplications in \left(a+1\right)\times 2\left(a+2\right)+3a.
\frac{2a^{2}+9a+4}{4a\left(a+2\right)}
Combine like terms in 2a^{2}+4a+2a+4+3a.
\frac{2a^{2}+9a+4}{4a^{2}+8a}
Expand 4a\left(a+2\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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\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}