Evaluate
\frac{4x}{x^{2}-4y^{2}}
Expand
-\frac{4x}{4y^{2}-x^{2}}
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\frac{3x-2y}{\left(x-2y\right)\left(x+2y\right)}+\frac{3}{3\left(x-2y\right)}
Factor x^{2}-4y^{2}. Factor 3x-6y.
\frac{3\left(3x-2y\right)}{3\left(x-2y\right)\left(x+2y\right)}+\frac{3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2y\right)\left(x+2y\right) and 3\left(x-2y\right) is 3\left(x-2y\right)\left(x+2y\right). Multiply \frac{3x-2y}{\left(x-2y\right)\left(x+2y\right)} times \frac{3}{3}. Multiply \frac{3}{3\left(x-2y\right)} times \frac{x+2y}{x+2y}.
\frac{3\left(3x-2y\right)+3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)}
Since \frac{3\left(3x-2y\right)}{3\left(x-2y\right)\left(x+2y\right)} and \frac{3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)} have the same denominator, add them by adding their numerators.
\frac{9x-6y+3x+6y}{3\left(x-2y\right)\left(x+2y\right)}
Do the multiplications in 3\left(3x-2y\right)+3\left(x+2y\right).
\frac{12x}{3\left(x-2y\right)\left(x+2y\right)}
Combine like terms in 9x-6y+3x+6y.
\frac{4x}{\left(x-2y\right)\left(x+2y\right)}
Cancel out 3 in both numerator and denominator.
\frac{4x}{x^{2}-4y^{2}}
Expand \left(x-2y\right)\left(x+2y\right).
\frac{3x-2y}{\left(x-2y\right)\left(x+2y\right)}+\frac{3}{3\left(x-2y\right)}
Factor x^{2}-4y^{2}. Factor 3x-6y.
\frac{3\left(3x-2y\right)}{3\left(x-2y\right)\left(x+2y\right)}+\frac{3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2y\right)\left(x+2y\right) and 3\left(x-2y\right) is 3\left(x-2y\right)\left(x+2y\right). Multiply \frac{3x-2y}{\left(x-2y\right)\left(x+2y\right)} times \frac{3}{3}. Multiply \frac{3}{3\left(x-2y\right)} times \frac{x+2y}{x+2y}.
\frac{3\left(3x-2y\right)+3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)}
Since \frac{3\left(3x-2y\right)}{3\left(x-2y\right)\left(x+2y\right)} and \frac{3\left(x+2y\right)}{3\left(x-2y\right)\left(x+2y\right)} have the same denominator, add them by adding their numerators.
\frac{9x-6y+3x+6y}{3\left(x-2y\right)\left(x+2y\right)}
Do the multiplications in 3\left(3x-2y\right)+3\left(x+2y\right).
\frac{12x}{3\left(x-2y\right)\left(x+2y\right)}
Combine like terms in 9x-6y+3x+6y.
\frac{4x}{\left(x-2y\right)\left(x+2y\right)}
Cancel out 3 in both numerator and denominator.
\frac{4x}{x^{2}-4y^{2}}
Expand \left(x-2y\right)\left(x+2y\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}