Evaluate
3\left(x+5\right)
Expand
3x+15
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\frac{\frac{4x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{4x}{x-3} times \frac{x+3}{x+3}. Multiply \frac{x}{x+3} times \frac{x-3}{x-3}.
\frac{\frac{4x\left(x+3\right)-x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Since \frac{4x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{4x^{2}+12x-x^{2}+3x}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Do the multiplications in 4x\left(x+3\right)-x\left(x-3\right).
\frac{\frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Combine like terms in 4x^{2}+12x-x^{2}+3x.
\frac{\left(3x^{2}+15x\right)\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)x}
Divide \frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)} by \frac{x}{x^{2}-9} by multiplying \frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x^{2}-9}.
\frac{3x\left(x-3\right)\left(x+3\right)\left(x+5\right)}{x\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
3\left(x+5\right)
Cancel out x\left(x-3\right)\left(x+3\right) in both numerator and denominator.
3x+15
Expand the expression.
\frac{\frac{4x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{4x}{x-3} times \frac{x+3}{x+3}. Multiply \frac{x}{x+3} times \frac{x-3}{x-3}.
\frac{\frac{4x\left(x+3\right)-x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Since \frac{4x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} and \frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{4x^{2}+12x-x^{2}+3x}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Do the multiplications in 4x\left(x+3\right)-x\left(x-3\right).
\frac{\frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)}}{\frac{x}{x^{2}-9}}
Combine like terms in 4x^{2}+12x-x^{2}+3x.
\frac{\left(3x^{2}+15x\right)\left(x^{2}-9\right)}{\left(x-3\right)\left(x+3\right)x}
Divide \frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)} by \frac{x}{x^{2}-9} by multiplying \frac{3x^{2}+15x}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{x}{x^{2}-9}.
\frac{3x\left(x-3\right)\left(x+3\right)\left(x+5\right)}{x\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
3\left(x+5\right)
Cancel out x\left(x-3\right)\left(x+3\right) in both numerator and denominator.
3x+15
Expand the expression.
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}