Evaluate
-\frac{16x^{2}}{1-4x^{2}}
Expand
-\frac{16x^{2}}{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{20x^{2}-1}{1-4x^{2}}
Multiply \frac{1-2x}{2x+1} times \frac{2x+1}{2x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{-\left(2x-1\right)\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}-\frac{20x^{2}-1}{1-4x^{2}}
Extract the negative sign in 1-2x.
-1-\frac{20x^{2}-1}{1-4x^{2}}
Cancel out \left(2x-1\right)\left(2x+1\right) in both numerator and denominator.
-1-\frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)}
Factor 1-4x^{2}.
-\frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)}-\frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)}.
\frac{-\left(-2x-1\right)\left(2x-1\right)-\left(20x^{2}-1\right)}{\left(-2x-1\right)\left(2x-1\right)}
Since -\frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)} and \frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-2x+2x-1-20x^{2}+1}{\left(-2x-1\right)\left(2x-1\right)}
Do the multiplications in -\left(-2x-1\right)\left(2x-1\right)-\left(20x^{2}-1\right).
\frac{-16x^{2}}{\left(-2x-1\right)\left(2x-1\right)}
Combine like terms in 4x^{2}-2x+2x-1-20x^{2}+1.
\frac{-16x^{2}}{-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{20x^{2}-1}{1-4x^{2}}
Multiply \frac{1-2x}{2x+1} times \frac{2x+1}{2x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{-\left(2x-1\right)\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}-\frac{20x^{2}-1}{1-4x^{2}}
Extract the negative sign in 1-2x.
-1-\frac{20x^{2}-1}{1-4x^{2}}
Cancel out \left(2x-1\right)\left(2x+1\right) in both numerator and denominator.
-1-\frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)}
Factor 1-4x^{2}.
-\frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)}-\frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)}.
\frac{-\left(-2x-1\right)\left(2x-1\right)-\left(20x^{2}-1\right)}{\left(-2x-1\right)\left(2x-1\right)}
Since -\frac{\left(-2x-1\right)\left(2x-1\right)}{\left(-2x-1\right)\left(2x-1\right)} and \frac{20x^{2}-1}{\left(-2x-1\right)\left(2x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-2x+2x-1-20x^{2}+1}{\left(-2x-1\right)\left(2x-1\right)}
Do the multiplications in -\left(-2x-1\right)\left(2x-1\right)-\left(20x^{2}-1\right).
\frac{-16x^{2}}{\left(-2x-1\right)\left(2x-1\right)}
Combine like terms in 4x^{2}-2x+2x-1-20x^{2}+1.
\frac{-16x^{2}}{-4x^{2}+1}
Expand \left(-2x-1\right)\left(2x-1\right).
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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