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