Evaluate
\frac{5\left(x-2\right)\left(2x+1\right)}{2\left(x-5\right)\left(x-1\right)}
Expand
\frac{5\left(2x^{2}-3x-2\right)}{2\left(x-5\right)\left(x-1\right)}
Graph
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\frac{\left(x-2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-1\right)}\times \frac{5}{2}
Multiply \frac{x-2}{x-5} times \frac{2x+1}{x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-2\right)\left(2x+1\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Multiply \frac{\left(x-2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-1\right)} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x^{2}+x-4x-2\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Apply the distributive property by multiplying each term of x-2 by each term of 2x+1.
\frac{\left(2x^{2}-3x-2\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Combine x and -4x to get -3x.
\frac{10x^{2}-15x-10}{\left(x-5\right)\left(x-1\right)\times 2}
Use the distributive property to multiply 2x^{2}-3x-2 by 5.
\frac{10x^{2}-15x-10}{\left(x^{2}-x-5x+5\right)\times 2}
Apply the distributive property by multiplying each term of x-5 by each term of x-1.
\frac{10x^{2}-15x-10}{\left(x^{2}-6x+5\right)\times 2}
Combine -x and -5x to get -6x.
\frac{10x^{2}-15x-10}{2x^{2}-12x+10}
Use the distributive property to multiply x^{2}-6x+5 by 2.
\frac{\left(x-2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-1\right)}\times \frac{5}{2}
Multiply \frac{x-2}{x-5} times \frac{2x+1}{x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-2\right)\left(2x+1\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Multiply \frac{\left(x-2\right)\left(2x+1\right)}{\left(x-5\right)\left(x-1\right)} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(2x^{2}+x-4x-2\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Apply the distributive property by multiplying each term of x-2 by each term of 2x+1.
\frac{\left(2x^{2}-3x-2\right)\times 5}{\left(x-5\right)\left(x-1\right)\times 2}
Combine x and -4x to get -3x.
\frac{10x^{2}-15x-10}{\left(x-5\right)\left(x-1\right)\times 2}
Use the distributive property to multiply 2x^{2}-3x-2 by 5.
\frac{10x^{2}-15x-10}{\left(x^{2}-x-5x+5\right)\times 2}
Apply the distributive property by multiplying each term of x-5 by each term of x-1.
\frac{10x^{2}-15x-10}{\left(x^{2}-6x+5\right)\times 2}
Combine -x and -5x to get -6x.
\frac{10x^{2}-15x-10}{2x^{2}-12x+10}
Use the distributive property to multiply x^{2}-6x+5 by 2.
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}