Evaluate
\frac{6\left(3x-20\right)}{x^{2}}
Expand
\frac{6\left(3x-20\right)}{x^{2}}
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\left(\frac{5\left(x-8\right)}{x\left(x-8\right)}+\frac{x}{x\left(x-8\right)}\right)\times \frac{3x-24}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-8 is x\left(x-8\right). Multiply \frac{5}{x} times \frac{x-8}{x-8}. Multiply \frac{1}{x-8} times \frac{x}{x}.
\frac{5\left(x-8\right)+x}{x\left(x-8\right)}\times \frac{3x-24}{x}
Since \frac{5\left(x-8\right)}{x\left(x-8\right)} and \frac{x}{x\left(x-8\right)} have the same denominator, add them by adding their numerators.
\frac{5x-40+x}{x\left(x-8\right)}\times \frac{3x-24}{x}
Do the multiplications in 5\left(x-8\right)+x.
\frac{6x-40}{x\left(x-8\right)}\times \frac{3x-24}{x}
Combine like terms in 5x-40+x.
\frac{\left(6x-40\right)\left(3x-24\right)}{x\left(x-8\right)x}
Multiply \frac{6x-40}{x\left(x-8\right)} times \frac{3x-24}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(6x-40\right)\left(3x-24\right)}{x^{2}\left(x-8\right)}
Multiply x and x to get x^{2}.
\frac{2\times 3\left(x-8\right)\left(3x-20\right)}{\left(x-8\right)x^{2}}
Factor the expressions that are not already factored.
\frac{2\times 3\left(3x-20\right)}{x^{2}}
Cancel out x-8 in both numerator and denominator.
\frac{18x-120}{x^{2}}
Expand the expression.
\left(\frac{5\left(x-8\right)}{x\left(x-8\right)}+\frac{x}{x\left(x-8\right)}\right)\times \frac{3x-24}{x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-8 is x\left(x-8\right). Multiply \frac{5}{x} times \frac{x-8}{x-8}. Multiply \frac{1}{x-8} times \frac{x}{x}.
\frac{5\left(x-8\right)+x}{x\left(x-8\right)}\times \frac{3x-24}{x}
Since \frac{5\left(x-8\right)}{x\left(x-8\right)} and \frac{x}{x\left(x-8\right)} have the same denominator, add them by adding their numerators.
\frac{5x-40+x}{x\left(x-8\right)}\times \frac{3x-24}{x}
Do the multiplications in 5\left(x-8\right)+x.
\frac{6x-40}{x\left(x-8\right)}\times \frac{3x-24}{x}
Combine like terms in 5x-40+x.
\frac{\left(6x-40\right)\left(3x-24\right)}{x\left(x-8\right)x}
Multiply \frac{6x-40}{x\left(x-8\right)} times \frac{3x-24}{x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(6x-40\right)\left(3x-24\right)}{x^{2}\left(x-8\right)}
Multiply x and x to get x^{2}.
\frac{2\times 3\left(x-8\right)\left(3x-20\right)}{\left(x-8\right)x^{2}}
Factor the expressions that are not already factored.
\frac{2\times 3\left(3x-20\right)}{x^{2}}
Cancel out x-8 in both numerator and denominator.
\frac{18x-120}{x^{2}}
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}