Evaluate
\frac{4h}{\left(2x+1\right)\left(2x+2h+1\right)}
Expand
\frac{4h}{\left(2x+1\right)\left(2x+2h+1\right)}
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\frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}-\frac{\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+h\right)+1 and 2x+1 is \left(2x+1\right)\left(2\left(x+h\right)+1\right). Multiply \frac{2\left(x+h\right)-1}{2\left(x+h\right)+1} times \frac{2x+1}{2x+1}. Multiply \frac{2x-1}{2x+1} times \frac{2\left(x+h\right)+1}{2\left(x+h\right)+1}.
\frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)-\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Since \frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)} and \frac{\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}+2x+4hx+2h-2x-1-4x^{2}-4xh-2x+2x+2h+1}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Do the multiplications in \left(2\left(x+h\right)-1\right)\left(2x+1\right)-\left(2x-1\right)\left(2\left(x+h\right)+1\right).
\frac{4h}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Combine like terms in 4x^{2}+2x+4hx+2h-2x-1-4x^{2}-4xh-2x+2x+2h+1.
\frac{4h}{4x^{2}+4hx+4x+2h+1}
Expand \left(2x+1\right)\left(2\left(x+h\right)+1\right).
\frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}-\frac{\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+h\right)+1 and 2x+1 is \left(2x+1\right)\left(2\left(x+h\right)+1\right). Multiply \frac{2\left(x+h\right)-1}{2\left(x+h\right)+1} times \frac{2x+1}{2x+1}. Multiply \frac{2x-1}{2x+1} times \frac{2\left(x+h\right)+1}{2\left(x+h\right)+1}.
\frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)-\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Since \frac{\left(2\left(x+h\right)-1\right)\left(2x+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)} and \frac{\left(2x-1\right)\left(2\left(x+h\right)+1\right)}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}+2x+4hx+2h-2x-1-4x^{2}-4xh-2x+2x+2h+1}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Do the multiplications in \left(2\left(x+h\right)-1\right)\left(2x+1\right)-\left(2x-1\right)\left(2\left(x+h\right)+1\right).
\frac{4h}{\left(2x+1\right)\left(2\left(x+h\right)+1\right)}
Combine like terms in 4x^{2}+2x+4hx+2h-2x-1-4x^{2}-4xh-2x+2x+2h+1.
\frac{4h}{4x^{2}+4hx+4x+2h+1}
Expand \left(2x+1\right)\left(2\left(x+h\right)+1\right).
Examples
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{ 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}