Evaluate
\frac{1}{1-9x^{2}}
Expand
-\frac{1}{9x^{2}-1}
Graph
Share
Copied to clipboard
\frac{\left(3+x\right)\left(-3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1+3x and 1-3x is \left(-3x+1\right)\left(3x+1\right). Multiply \frac{3+x}{1+3x} times \frac{-3x+1}{-3x+1}. Multiply \frac{3-x}{1-3x} times \frac{3x+1}{3x+1}.
\frac{\left(3+x\right)\left(-3x+1\right)-\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Since \frac{\left(3+x\right)\left(-3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)} and \frac{\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{-9x+3-3x^{2}+x-9x-3+3x^{2}+x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Do the multiplications in \left(3+x\right)\left(-3x+1\right)-\left(3-x\right)\left(3x+1\right).
\frac{-16x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Combine like terms in -9x+3-3x^{2}+x-9x-3+3x^{2}+x.
\frac{-16x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{\left(3x-1\right)\left(3x+1\right)}
Factor 9x^{2}-1.
\frac{-\left(-16\right)x}{\left(3x-1\right)\left(3x+1\right)}-\frac{1+16x}{\left(3x-1\right)\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(-3x+1\right)\left(3x+1\right) and \left(3x-1\right)\left(3x+1\right) is \left(3x-1\right)\left(3x+1\right). Multiply \frac{-16x}{\left(-3x+1\right)\left(3x+1\right)} times \frac{-1}{-1}.
\frac{-\left(-16\right)x-\left(1+16x\right)}{\left(3x-1\right)\left(3x+1\right)}
Since \frac{-\left(-16\right)x}{\left(3x-1\right)\left(3x+1\right)} and \frac{1+16x}{\left(3x-1\right)\left(3x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{16x-1-16x}{\left(3x-1\right)\left(3x+1\right)}
Do the multiplications in -\left(-16\right)x-\left(1+16x\right).
\frac{-1}{\left(3x-1\right)\left(3x+1\right)}
Combine like terms in 16x-1-16x.
\frac{-1}{9x^{2}-1}
Expand \left(3x-1\right)\left(3x+1\right).
\frac{\left(3+x\right)\left(-3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1+3x and 1-3x is \left(-3x+1\right)\left(3x+1\right). Multiply \frac{3+x}{1+3x} times \frac{-3x+1}{-3x+1}. Multiply \frac{3-x}{1-3x} times \frac{3x+1}{3x+1}.
\frac{\left(3+x\right)\left(-3x+1\right)-\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Since \frac{\left(3+x\right)\left(-3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)} and \frac{\left(3-x\right)\left(3x+1\right)}{\left(-3x+1\right)\left(3x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{-9x+3-3x^{2}+x-9x-3+3x^{2}+x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Do the multiplications in \left(3+x\right)\left(-3x+1\right)-\left(3-x\right)\left(3x+1\right).
\frac{-16x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{9x^{2}-1}
Combine like terms in -9x+3-3x^{2}+x-9x-3+3x^{2}+x.
\frac{-16x}{\left(-3x+1\right)\left(3x+1\right)}-\frac{1+16x}{\left(3x-1\right)\left(3x+1\right)}
Factor 9x^{2}-1.
\frac{-\left(-16\right)x}{\left(3x-1\right)\left(3x+1\right)}-\frac{1+16x}{\left(3x-1\right)\left(3x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(-3x+1\right)\left(3x+1\right) and \left(3x-1\right)\left(3x+1\right) is \left(3x-1\right)\left(3x+1\right). Multiply \frac{-16x}{\left(-3x+1\right)\left(3x+1\right)} times \frac{-1}{-1}.
\frac{-\left(-16\right)x-\left(1+16x\right)}{\left(3x-1\right)\left(3x+1\right)}
Since \frac{-\left(-16\right)x}{\left(3x-1\right)\left(3x+1\right)} and \frac{1+16x}{\left(3x-1\right)\left(3x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{16x-1-16x}{\left(3x-1\right)\left(3x+1\right)}
Do the multiplications in -\left(-16\right)x-\left(1+16x\right).
\frac{-1}{\left(3x-1\right)\left(3x+1\right)}
Combine like terms in 16x-1-16x.
\frac{-1}{9x^{2}-1}
Expand \left(3x-1\right)\left(3x+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}