Evaluate
\frac{23y}{6x}+\frac{9}{2}
Expand
\frac{23y}{6x}+\frac{9}{2}
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\frac{2\times 2x}{2x}+\frac{9x+5y}{2x}-\frac{6x-4y}{3x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2x}{2x}.
\frac{2\times 2x+9x+5y}{2x}-\frac{6x-4y}{3x}
Since \frac{2\times 2x}{2x} and \frac{9x+5y}{2x} have the same denominator, add them by adding their numerators.
\frac{4x+9x+5y}{2x}-\frac{6x-4y}{3x}
Do the multiplications in 2\times 2x+9x+5y.
\frac{13x+5y}{2x}-\frac{6x-4y}{3x}
Combine like terms in 4x+9x+5y.
\frac{3\left(13x+5y\right)}{6x}-\frac{2\left(6x-4y\right)}{6x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 3x is 6x. Multiply \frac{13x+5y}{2x} times \frac{3}{3}. Multiply \frac{6x-4y}{3x} times \frac{2}{2}.
\frac{3\left(13x+5y\right)-2\left(6x-4y\right)}{6x}
Since \frac{3\left(13x+5y\right)}{6x} and \frac{2\left(6x-4y\right)}{6x} have the same denominator, subtract them by subtracting their numerators.
\frac{39x+15y-12x+8y}{6x}
Do the multiplications in 3\left(13x+5y\right)-2\left(6x-4y\right).
\frac{27x+23y}{6x}
Combine like terms in 39x+15y-12x+8y.
\frac{2\times 2x}{2x}+\frac{9x+5y}{2x}-\frac{6x-4y}{3x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2x}{2x}.
\frac{2\times 2x+9x+5y}{2x}-\frac{6x-4y}{3x}
Since \frac{2\times 2x}{2x} and \frac{9x+5y}{2x} have the same denominator, add them by adding their numerators.
\frac{4x+9x+5y}{2x}-\frac{6x-4y}{3x}
Do the multiplications in 2\times 2x+9x+5y.
\frac{13x+5y}{2x}-\frac{6x-4y}{3x}
Combine like terms in 4x+9x+5y.
\frac{3\left(13x+5y\right)}{6x}-\frac{2\left(6x-4y\right)}{6x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 3x is 6x. Multiply \frac{13x+5y}{2x} times \frac{3}{3}. Multiply \frac{6x-4y}{3x} times \frac{2}{2}.
\frac{3\left(13x+5y\right)-2\left(6x-4y\right)}{6x}
Since \frac{3\left(13x+5y\right)}{6x} and \frac{2\left(6x-4y\right)}{6x} have the same denominator, subtract them by subtracting their numerators.
\frac{39x+15y-12x+8y}{6x}
Do the multiplications in 3\left(13x+5y\right)-2\left(6x-4y\right).
\frac{27x+23y}{6x}
Combine like terms in 39x+15y-12x+8y.
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}