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