Evaluate
\frac{\left(x-4\right)\left(2x+5\right)}{\left(6x-1\right)x^{2}}
Expand
\frac{2x^{2}-3x-20}{\left(6x-1\right)x^{2}}
Graph
Share
Copied to clipboard
\frac{\left(2x-5\right)\left(2x+5\right)}{\left(2x-5\right)x^{2}}\times \frac{x^{2}-2x-8}{6x^{2}+11x-2}
Factor the expressions that are not already factored in \frac{4x^{2}-25}{2x^{3}-5x^{2}}.
\frac{2x+5}{x^{2}}\times \frac{x^{2}-2x-8}{6x^{2}+11x-2}
Cancel out 2x-5 in both numerator and denominator.
\frac{2x+5}{x^{2}}\times \frac{\left(x-4\right)\left(x+2\right)}{\left(6x-1\right)\left(x+2\right)}
Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{6x^{2}+11x-2}.
\frac{2x+5}{x^{2}}\times \frac{x-4}{6x-1}
Cancel out x+2 in both numerator and denominator.
\frac{\left(2x+5\right)\left(x-4\right)}{x^{2}\left(6x-1\right)}
Multiply \frac{2x+5}{x^{2}} times \frac{x-4}{6x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{2x^{2}-3x-20}{x^{2}\left(6x-1\right)}
Use the distributive property to multiply 2x+5 by x-4 and combine like terms.
\frac{2x^{2}-3x-20}{6x^{3}-x^{2}}
Use the distributive property to multiply x^{2} by 6x-1.
\frac{\left(2x-5\right)\left(2x+5\right)}{\left(2x-5\right)x^{2}}\times \frac{x^{2}-2x-8}{6x^{2}+11x-2}
Factor the expressions that are not already factored in \frac{4x^{2}-25}{2x^{3}-5x^{2}}.
\frac{2x+5}{x^{2}}\times \frac{x^{2}-2x-8}{6x^{2}+11x-2}
Cancel out 2x-5 in both numerator and denominator.
\frac{2x+5}{x^{2}}\times \frac{\left(x-4\right)\left(x+2\right)}{\left(6x-1\right)\left(x+2\right)}
Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{6x^{2}+11x-2}.
\frac{2x+5}{x^{2}}\times \frac{x-4}{6x-1}
Cancel out x+2 in both numerator and denominator.
\frac{\left(2x+5\right)\left(x-4\right)}{x^{2}\left(6x-1\right)}
Multiply \frac{2x+5}{x^{2}} times \frac{x-4}{6x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{2x^{2}-3x-20}{x^{2}\left(6x-1\right)}
Use the distributive property to multiply 2x+5 by x-4 and combine like terms.
\frac{2x^{2}-3x-20}{6x^{3}-x^{2}}
Use the distributive property to multiply x^{2} by 6x-1.
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}