Evaluate
\frac{x^{3}-20x^{2}+33x-56}{\left(x-3\right)\left(x+7\right)}
Expand
\frac{x^{3}-20x^{2}+33x-56}{\left(x-3\right)\left(x+7\right)}
Graph
Quiz
Polynomial
5 problems similar to:
\frac { x ^ { 2 } - 16 x } { x + 7 } - \frac { x + 8 } { x - 3 }
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\frac{\left(x^{2}-16x\right)\left(x-3\right)}{\left(x-3\right)\left(x+7\right)}-\frac{\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+7 and x-3 is \left(x-3\right)\left(x+7\right). Multiply \frac{x^{2}-16x}{x+7} times \frac{x-3}{x-3}. Multiply \frac{x+8}{x-3} times \frac{x+7}{x+7}.
\frac{\left(x^{2}-16x\right)\left(x-3\right)-\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)}
Since \frac{\left(x^{2}-16x\right)\left(x-3\right)}{\left(x-3\right)\left(x+7\right)} and \frac{\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}-3x^{2}-16x^{2}+48x-x^{2}-7x-8x-56}{\left(x-3\right)\left(x+7\right)}
Do the multiplications in \left(x^{2}-16x\right)\left(x-3\right)-\left(x+8\right)\left(x+7\right).
\frac{x^{3}-20x^{2}+33x-56}{\left(x-3\right)\left(x+7\right)}
Combine like terms in x^{3}-3x^{2}-16x^{2}+48x-x^{2}-7x-8x-56.
\frac{x^{3}-20x^{2}+33x-56}{x^{2}+4x-21}
Expand \left(x-3\right)\left(x+7\right).
\frac{\left(x^{2}-16x\right)\left(x-3\right)}{\left(x-3\right)\left(x+7\right)}-\frac{\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+7 and x-3 is \left(x-3\right)\left(x+7\right). Multiply \frac{x^{2}-16x}{x+7} times \frac{x-3}{x-3}. Multiply \frac{x+8}{x-3} times \frac{x+7}{x+7}.
\frac{\left(x^{2}-16x\right)\left(x-3\right)-\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)}
Since \frac{\left(x^{2}-16x\right)\left(x-3\right)}{\left(x-3\right)\left(x+7\right)} and \frac{\left(x+8\right)\left(x+7\right)}{\left(x-3\right)\left(x+7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}-3x^{2}-16x^{2}+48x-x^{2}-7x-8x-56}{\left(x-3\right)\left(x+7\right)}
Do the multiplications in \left(x^{2}-16x\right)\left(x-3\right)-\left(x+8\right)\left(x+7\right).
\frac{x^{3}-20x^{2}+33x-56}{\left(x-3\right)\left(x+7\right)}
Combine like terms in x^{3}-3x^{2}-16x^{2}+48x-x^{2}-7x-8x-56.
\frac{x^{3}-20x^{2}+33x-56}{x^{2}+4x-21}
Expand \left(x-3\right)\left(x+7\right).
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\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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