Evaluate
\frac{4\times \left(\frac{x}{x+3}\right)^{2}}{x-3}
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\frac{4\times \left(\frac{x}{x+3}\right)^{2}}{x-3}
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\frac{x+1}{x-3}-\frac{6}{\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Factor x^{2}+6x+9.
\frac{\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x+3\right)^{2} is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x+1}{x-3} times \frac{\left(x+3\right)^{2}}{\left(x+3\right)^{2}}. Multiply \frac{6}{\left(x+3\right)^{2}} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)^{2}-6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Since \frac{\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+6x^{2}+9x+x^{2}+6x+9-6x+18}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Do the multiplications in \left(x+1\right)\left(x+3\right)^{2}-6\left(x-3\right).
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Combine like terms in x^{3}+6x^{2}+9x+x^{2}+6x+9-6x+18.
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right)^{2} and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)} times \frac{x+3}{x+3}.
\frac{x^{3}+7x^{2}+9x+27-\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
Since \frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+7x^{2}+9x+27-x^{3}-3x^{2}-9x-27}{\left(x-3\right)\left(x+3\right)^{2}}
Do the multiplications in x^{3}+7x^{2}+9x+27-\left(x^{2}+9\right)\left(x+3\right).
\frac{4x^{2}}{\left(x-3\right)\left(x+3\right)^{2}}
Combine like terms in x^{3}+7x^{2}+9x+27-x^{3}-3x^{2}-9x-27.
\frac{4x^{2}}{x^{3}+3x^{2}-9x-27}
Expand \left(x-3\right)\left(x+3\right)^{2}.
\frac{x+1}{x-3}-\frac{6}{\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Factor x^{2}+6x+9.
\frac{\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x+3\right)^{2} is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x+1}{x-3} times \frac{\left(x+3\right)^{2}}{\left(x+3\right)^{2}}. Multiply \frac{6}{\left(x+3\right)^{2}} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)^{2}-6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Since \frac{\left(x+1\right)\left(x+3\right)^{2}}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{6\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+6x^{2}+9x+x^{2}+6x+9-6x+18}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Do the multiplications in \left(x+1\right)\left(x+3\right)^{2}-6\left(x-3\right).
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{x^{2}-9}
Combine like terms in x^{3}+6x^{2}+9x+x^{2}+6x+9-6x+18.
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}-9.
\frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right)^{2} and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)} times \frac{x+3}{x+3}.
\frac{x^{3}+7x^{2}+9x+27-\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
Since \frac{x^{3}+7x^{2}+9x+27}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{\left(x^{2}+9\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+7x^{2}+9x+27-x^{3}-3x^{2}-9x-27}{\left(x-3\right)\left(x+3\right)^{2}}
Do the multiplications in x^{3}+7x^{2}+9x+27-\left(x^{2}+9\right)\left(x+3\right).
\frac{4x^{2}}{\left(x-3\right)\left(x+3\right)^{2}}
Combine like terms in x^{3}+7x^{2}+9x+27-x^{3}-3x^{2}-9x-27.
\frac{4x^{2}}{x^{3}+3x^{2}-9x-27}
Expand \left(x-3\right)\left(x+3\right)^{2}.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
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Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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