Evaluate
\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}
Expand
\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}
Graph
Quiz
Polynomial
5 problems similar to:
\frac{ x+1 }{ { x }^{ 2 } -9 } - \frac{ x-1 }{ { x }^{ 2 } +6x+9 }
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\frac{x+1}{\left(x-3\right)\left(x+3\right)}-\frac{x-1}{\left(x+3\right)^{2}}
Factor x^{2}-9. Factor x^{2}+6x+9.
\frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{\left(x-1\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) and \left(x+3\right)^{2} is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x+1}{\left(x-3\right)\left(x+3\right)} times \frac{x+3}{x+3}. Multiply \frac{x-1}{\left(x+3\right)^{2}} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
Since \frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{\left(x-1\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^{2}+3x+x+3-x^{2}+3x+x-3}{\left(x-3\right)\left(x+3\right)^{2}}
Do the multiplications in \left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right).
\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}
Combine like terms in x^{2}+3x+x+3-x^{2}+3x+x-3.
\frac{8x}{x^{3}+3x^{2}-9x-27}
Expand \left(x-3\right)\left(x+3\right)^{2}.
\frac{x+1}{\left(x-3\right)\left(x+3\right)}-\frac{x-1}{\left(x+3\right)^{2}}
Factor x^{2}-9. Factor x^{2}+6x+9.
\frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{\left(x-1\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) and \left(x+3\right)^{2} is \left(x-3\right)\left(x+3\right)^{2}. Multiply \frac{x+1}{\left(x-3\right)\left(x+3\right)} times \frac{x+3}{x+3}. Multiply \frac{x-1}{\left(x+3\right)^{2}} times \frac{x-3}{x-3}.
\frac{\left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}
Since \frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} and \frac{\left(x-1\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^{2}+3x+x+3-x^{2}+3x+x-3}{\left(x-3\right)\left(x+3\right)^{2}}
Do the multiplications in \left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right).
\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}
Combine like terms in x^{2}+3x+x+3-x^{2}+3x+x-3.
\frac{8x}{x^{3}+3x^{2}-9x-27}
Expand \left(x-3\right)\left(x+3\right)^{2}.
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
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\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}