Evaluate
\frac{2x^{2}+7x+4}{\left(x-4\right)\left(x+3\right)}
Expand
\frac{2x^{2}+7x+4}{\left(x-4\right)\left(x+3\right)}
Graph
Quiz
Polynomial
5 problems similar to:
\frac { x + 4 } { x ^ { 2 } - x - 12 } + \frac { 2 x } { x - 4 }
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\frac{x+4}{\left(x-4\right)\left(x+3\right)}+\frac{2x}{x-4}
Factor x^{2}-x-12.
\frac{x+4}{\left(x-4\right)\left(x+3\right)}+\frac{2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+3\right) and x-4 is \left(x-4\right)\left(x+3\right). Multiply \frac{2x}{x-4} times \frac{x+3}{x+3}.
\frac{x+4+2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}
Since \frac{x+4}{\left(x-4\right)\left(x+3\right)} and \frac{2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{x+4+2x^{2}+6x}{\left(x-4\right)\left(x+3\right)}
Do the multiplications in x+4+2x\left(x+3\right).
\frac{7x+4+2x^{2}}{\left(x-4\right)\left(x+3\right)}
Combine like terms in x+4+2x^{2}+6x.
\frac{7x+4+2x^{2}}{x^{2}-x-12}
Expand \left(x-4\right)\left(x+3\right).
\frac{x+4}{\left(x-4\right)\left(x+3\right)}+\frac{2x}{x-4}
Factor x^{2}-x-12.
\frac{x+4}{\left(x-4\right)\left(x+3\right)}+\frac{2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+3\right) and x-4 is \left(x-4\right)\left(x+3\right). Multiply \frac{2x}{x-4} times \frac{x+3}{x+3}.
\frac{x+4+2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}
Since \frac{x+4}{\left(x-4\right)\left(x+3\right)} and \frac{2x\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{x+4+2x^{2}+6x}{\left(x-4\right)\left(x+3\right)}
Do the multiplications in x+4+2x\left(x+3\right).
\frac{7x+4+2x^{2}}{\left(x-4\right)\left(x+3\right)}
Combine like terms in x+4+2x^{2}+6x.
\frac{7x+4+2x^{2}}{x^{2}-x-12}
Expand \left(x-4\right)\left(x+3\right).
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\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}