Evaluate
\frac{6x^{2}-9x-2}{\left(x-1\right)\left(9x^{2}-4\right)}
Expand
\frac{6x^{2}-9x-2}{\left(x-1\right)\left(9x^{2}-4\right)}
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\frac{12x^{2}-12x+4}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}-\frac{\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3x-2\right)\left(3x+2\right)\left(x-1\right) and \left(3x-2\right)\left(x-1\right) is \left(x-1\right)\left(3x-2\right)\left(3x+2\right). Multiply \frac{x+1}{\left(3x-2\right)\left(x-1\right)} times \frac{3x+2}{3x+2}.
\frac{12x^{2}-12x+4-\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Since \frac{12x^{2}-12x+4}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} and \frac{\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12x^{2}-12x+4-3x^{2}-2x-3x-2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Do the multiplications in 12x^{2}-12x+4-\left(x+1\right)\left(3x+2\right).
\frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Combine like terms in 12x^{2}-12x+4-3x^{2}-2x-3x-2.
\frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(3x-2\right)\left(3x+2\right) and \left(3x+2\right)\left(x-1\right) is \left(x-1\right)\left(3x-2\right)\left(3x+2\right). Multiply \frac{2-x}{\left(3x+2\right)\left(x-1\right)} times \frac{3x-2}{3x-2}.
\frac{9x^{2}-17x+2+\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Since \frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} and \frac{\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} have the same denominator, add them by adding their numerators.
\frac{9x^{2}-17x+2+6x-4-3x^{2}+2x}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Do the multiplications in 9x^{2}-17x+2+\left(2-x\right)\left(3x-2\right).
\frac{6x^{2}-9x-2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Combine like terms in 9x^{2}-17x+2+6x-4-3x^{2}+2x.
\frac{6x^{2}-9x-2}{9x^{3}-9x^{2}-4x+4}
Expand \left(x-1\right)\left(3x-2\right)\left(3x+2\right).
\frac{12x^{2}-12x+4}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}-\frac{\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3x-2\right)\left(3x+2\right)\left(x-1\right) and \left(3x-2\right)\left(x-1\right) is \left(x-1\right)\left(3x-2\right)\left(3x+2\right). Multiply \frac{x+1}{\left(3x-2\right)\left(x-1\right)} times \frac{3x+2}{3x+2}.
\frac{12x^{2}-12x+4-\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Since \frac{12x^{2}-12x+4}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} and \frac{\left(x+1\right)\left(3x+2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{12x^{2}-12x+4-3x^{2}-2x-3x-2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Do the multiplications in 12x^{2}-12x+4-\left(x+1\right)\left(3x+2\right).
\frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{2-x}{\left(3x+2\right)\left(x-1\right)}
Combine like terms in 12x^{2}-12x+4-3x^{2}-2x-3x-2.
\frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}+\frac{\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(3x-2\right)\left(3x+2\right) and \left(3x+2\right)\left(x-1\right) is \left(x-1\right)\left(3x-2\right)\left(3x+2\right). Multiply \frac{2-x}{\left(3x+2\right)\left(x-1\right)} times \frac{3x-2}{3x-2}.
\frac{9x^{2}-17x+2+\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Since \frac{9x^{2}-17x+2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} and \frac{\left(2-x\right)\left(3x-2\right)}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)} have the same denominator, add them by adding their numerators.
\frac{9x^{2}-17x+2+6x-4-3x^{2}+2x}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Do the multiplications in 9x^{2}-17x+2+\left(2-x\right)\left(3x-2\right).
\frac{6x^{2}-9x-2}{\left(x-1\right)\left(3x-2\right)\left(3x+2\right)}
Combine like terms in 9x^{2}-17x+2+6x-4-3x^{2}+2x.
\frac{6x^{2}-9x-2}{9x^{3}-9x^{2}-4x+4}
Expand \left(x-1\right)\left(3x-2\right)\left(3x+2\right).
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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