Evaluate
\frac{\left(x-1\right)\left(x^{2}+6x+15\right)}{x^{2}\left(x^{2}-9\right)}
Expand
\frac{x^{3}+5x^{2}+9x-15}{x^{2}\left(x^{2}-9\right)}
Graph
Share
Copied to clipboard
\frac{\frac{x+4}{x\left(x-3\right)}-\frac{1}{x\left(x+3\right)}}{\frac{x}{x-1}}
Factor x^{2}-3x. Factor 3x+x^{2}.
\frac{\frac{\left(x+4\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)}-\frac{x-3}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-3\right) and x\left(x+3\right) is x\left(x-3\right)\left(x+3\right). Multiply \frac{x+4}{x\left(x-3\right)} times \frac{x+3}{x+3}. Multiply \frac{1}{x\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{\frac{\left(x+4\right)\left(x+3\right)-\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Since \frac{\left(x+4\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)} and \frac{x-3}{x\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3x+x^{2}+4x+12-x+3}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Do the multiplications in \left(x+4\right)\left(x+3\right)-\left(x-3\right).
\frac{\frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Combine like terms in 3x+x^{2}+4x+12-x+3.
\frac{\left(6x+x^{2}+15\right)\left(x-1\right)}{x\left(x-3\right)\left(x+3\right)x}
Divide \frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)} by \frac{x}{x-1} by multiplying \frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x-1}.
\frac{\left(6x+x^{2}+15\right)\left(x-1\right)}{x^{2}\left(x-3\right)\left(x+3\right)}
Multiply x and x to get x^{2}.
\frac{5x^{2}+9x+x^{3}-15}{x^{2}\left(x-3\right)\left(x+3\right)}
Use the distributive property to multiply 6x+x^{2}+15 by x-1 and combine like terms.
\frac{5x^{2}+9x+x^{3}-15}{\left(x^{3}-3x^{2}\right)\left(x+3\right)}
Use the distributive property to multiply x^{2} by x-3.
\frac{5x^{2}+9x+x^{3}-15}{x^{4}-9x^{2}}
Use the distributive property to multiply x^{3}-3x^{2} by x+3 and combine like terms.
\frac{\frac{x+4}{x\left(x-3\right)}-\frac{1}{x\left(x+3\right)}}{\frac{x}{x-1}}
Factor x^{2}-3x. Factor 3x+x^{2}.
\frac{\frac{\left(x+4\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)}-\frac{x-3}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-3\right) and x\left(x+3\right) is x\left(x-3\right)\left(x+3\right). Multiply \frac{x+4}{x\left(x-3\right)} times \frac{x+3}{x+3}. Multiply \frac{1}{x\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{\frac{\left(x+4\right)\left(x+3\right)-\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Since \frac{\left(x+4\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)} and \frac{x-3}{x\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3x+x^{2}+4x+12-x+3}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Do the multiplications in \left(x+4\right)\left(x+3\right)-\left(x-3\right).
\frac{\frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)}}{\frac{x}{x-1}}
Combine like terms in 3x+x^{2}+4x+12-x+3.
\frac{\left(6x+x^{2}+15\right)\left(x-1\right)}{x\left(x-3\right)\left(x+3\right)x}
Divide \frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)} by \frac{x}{x-1} by multiplying \frac{6x+x^{2}+15}{x\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x-1}.
\frac{\left(6x+x^{2}+15\right)\left(x-1\right)}{x^{2}\left(x-3\right)\left(x+3\right)}
Multiply x and x to get x^{2}.
\frac{5x^{2}+9x+x^{3}-15}{x^{2}\left(x-3\right)\left(x+3\right)}
Use the distributive property to multiply 6x+x^{2}+15 by x-1 and combine like terms.
\frac{5x^{2}+9x+x^{3}-15}{\left(x^{3}-3x^{2}\right)\left(x+3\right)}
Use the distributive property to multiply x^{2} by x-3.
\frac{5x^{2}+9x+x^{3}-15}{x^{4}-9x^{2}}
Use the distributive property to multiply x^{3}-3x^{2} by x+3 and combine like terms.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\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}