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