Evaluate
\frac{2x+3}{2\left(3x-5\right)}
Expand
\frac{2x+3}{2\left(3x-5\right)}
Graph
Share
Copied to clipboard
\frac{2\left(2x-1\right)\left(4x-3\right)}{x\left(4x-3\right)\left(3x+4\right)}\times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20}
Factor the expressions that are not already factored in \frac{16x^{2}-20x+6}{12x^{3}+7x^{2}-12x}.
\frac{2\left(2x-1\right)}{x\left(3x+4\right)}\times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20}
Cancel out 4x-3 in both numerator and denominator.
\frac{2\left(2x-1\right)\left(6x^{3}+17x^{2}+12x\right)}{x\left(3x+4\right)\left(24x^{2}-52x+20\right)}
Multiply \frac{2\left(2x-1\right)}{x\left(3x+4\right)} times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20} by multiplying numerator times numerator and denominator times denominator.
\frac{2x\left(2x-1\right)\left(2x+3\right)\left(3x+4\right)}{4x\left(2x-1\right)\left(3x-5\right)\left(3x+4\right)}
Factor the expressions that are not already factored.
\frac{2x+3}{2\left(3x-5\right)}
Cancel out 2x\left(2x-1\right)\left(3x+4\right) in both numerator and denominator.
\frac{2x+3}{6x-10}
Expand the expression.
\frac{2\left(2x-1\right)\left(4x-3\right)}{x\left(4x-3\right)\left(3x+4\right)}\times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20}
Factor the expressions that are not already factored in \frac{16x^{2}-20x+6}{12x^{3}+7x^{2}-12x}.
\frac{2\left(2x-1\right)}{x\left(3x+4\right)}\times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20}
Cancel out 4x-3 in both numerator and denominator.
\frac{2\left(2x-1\right)\left(6x^{3}+17x^{2}+12x\right)}{x\left(3x+4\right)\left(24x^{2}-52x+20\right)}
Multiply \frac{2\left(2x-1\right)}{x\left(3x+4\right)} times \frac{6x^{3}+17x^{2}+12x}{24x^{2}-52x+20} by multiplying numerator times numerator and denominator times denominator.
\frac{2x\left(2x-1\right)\left(2x+3\right)\left(3x+4\right)}{4x\left(2x-1\right)\left(3x-5\right)\left(3x+4\right)}
Factor the expressions that are not already factored.
\frac{2x+3}{2\left(3x-5\right)}
Cancel out 2x\left(2x-1\right)\left(3x+4\right) in both numerator and denominator.
\frac{2x+3}{6x-10}
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}