Evaluate
\frac{6x^{2}+16x-5}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Expand
\frac{6x^{2}+16x-5}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Graph
Quiz
Polynomial
\frac { 7 x + 19 } { 3 x ^ { 2 } + 10 x - 8 } - \frac { x + 6 } { 3 x ^ { 2 } + x - 2 }
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\frac{7x+19}{\left(3x-2\right)\left(x+4\right)}-\frac{x+6}{\left(3x-2\right)\left(x+1\right)}
Factor 3x^{2}+10x-8. Factor 3x^{2}+x-2.
\frac{\left(7x+19\right)\left(x+1\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}-\frac{\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3x-2\right)\left(x+4\right) and \left(3x-2\right)\left(x+1\right) is \left(3x-2\right)\left(x+1\right)\left(x+4\right). Multiply \frac{7x+19}{\left(3x-2\right)\left(x+4\right)} times \frac{x+1}{x+1}. Multiply \frac{x+6}{\left(3x-2\right)\left(x+1\right)} times \frac{x+4}{x+4}.
\frac{\left(7x+19\right)\left(x+1\right)-\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Since \frac{\left(7x+19\right)\left(x+1\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)} and \frac{\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{7x^{2}+7x+19x+19-x^{2}-4x-6x-24}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Do the multiplications in \left(7x+19\right)\left(x+1\right)-\left(x+6\right)\left(x+4\right).
\frac{6x^{2}+16x-5}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Combine like terms in 7x^{2}+7x+19x+19-x^{2}-4x-6x-24.
\frac{6x^{2}+16x-5}{3x^{3}+13x^{2}+2x-8}
Expand \left(3x-2\right)\left(x+1\right)\left(x+4\right).
\frac{7x+19}{\left(3x-2\right)\left(x+4\right)}-\frac{x+6}{\left(3x-2\right)\left(x+1\right)}
Factor 3x^{2}+10x-8. Factor 3x^{2}+x-2.
\frac{\left(7x+19\right)\left(x+1\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}-\frac{\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3x-2\right)\left(x+4\right) and \left(3x-2\right)\left(x+1\right) is \left(3x-2\right)\left(x+1\right)\left(x+4\right). Multiply \frac{7x+19}{\left(3x-2\right)\left(x+4\right)} times \frac{x+1}{x+1}. Multiply \frac{x+6}{\left(3x-2\right)\left(x+1\right)} times \frac{x+4}{x+4}.
\frac{\left(7x+19\right)\left(x+1\right)-\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Since \frac{\left(7x+19\right)\left(x+1\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)} and \frac{\left(x+6\right)\left(x+4\right)}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{7x^{2}+7x+19x+19-x^{2}-4x-6x-24}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Do the multiplications in \left(7x+19\right)\left(x+1\right)-\left(x+6\right)\left(x+4\right).
\frac{6x^{2}+16x-5}{\left(3x-2\right)\left(x+1\right)\left(x+4\right)}
Combine like terms in 7x^{2}+7x+19x+19-x^{2}-4x-6x-24.
\frac{6x^{2}+16x-5}{3x^{3}+13x^{2}+2x-8}
Expand \left(3x-2\right)\left(x+1\right)\left(x+4\right).
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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
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