Evaluate
\frac{3x+2}{4x\left(x-2\right)}
Expand
\frac{3x+2}{4x\left(x-2\right)}
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\frac{\frac{16x}{x\left(x-2\right)}-\frac{4\left(x-2\right)}{x\left(x-2\right)}}{16}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x is x\left(x-2\right). Multiply \frac{16}{x-2} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{x-2}{x-2}.
\frac{\frac{16x-4\left(x-2\right)}{x\left(x-2\right)}}{16}
Since \frac{16x}{x\left(x-2\right)} and \frac{4\left(x-2\right)}{x\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{16x-4x+8}{x\left(x-2\right)}}{16}
Do the multiplications in 16x-4\left(x-2\right).
\frac{\frac{12x+8}{x\left(x-2\right)}}{16}
Combine like terms in 16x-4x+8.
\frac{12x+8}{x\left(x-2\right)\times 16}
Express \frac{\frac{12x+8}{x\left(x-2\right)}}{16} as a single fraction.
\frac{4\left(3x+2\right)}{16x\left(x-2\right)}
Factor the expressions that are not already factored.
\frac{3x+2}{4x\left(x-2\right)}
Cancel out 4 in both numerator and denominator.
\frac{3x+2}{4x^{2}-8x}
Expand the expression.
\frac{\frac{16x}{x\left(x-2\right)}-\frac{4\left(x-2\right)}{x\left(x-2\right)}}{16}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x is x\left(x-2\right). Multiply \frac{16}{x-2} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{x-2}{x-2}.
\frac{\frac{16x-4\left(x-2\right)}{x\left(x-2\right)}}{16}
Since \frac{16x}{x\left(x-2\right)} and \frac{4\left(x-2\right)}{x\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{16x-4x+8}{x\left(x-2\right)}}{16}
Do the multiplications in 16x-4\left(x-2\right).
\frac{\frac{12x+8}{x\left(x-2\right)}}{16}
Combine like terms in 16x-4x+8.
\frac{12x+8}{x\left(x-2\right)\times 16}
Express \frac{\frac{12x+8}{x\left(x-2\right)}}{16} as a single fraction.
\frac{4\left(3x+2\right)}{16x\left(x-2\right)}
Factor the expressions that are not already factored.
\frac{3x+2}{4x\left(x-2\right)}
Cancel out 4 in both numerator and denominator.
\frac{3x+2}{4x^{2}-8x}
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}