Evaluate
\frac{4x+7}{x\left(x-5\right)\left(x+7\right)}
Differentiate w.r.t. x
\frac{245-28x-29x^{2}-8x^{3}}{\left(x\left(x-5\right)\left(x+7\right)\right)^{2}}
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\frac{1}{x\left(x-5\right)}+\frac{3}{\left(x-5\right)\left(x+7\right)}
Factor x^{2}-5x. Factor x^{2}+2x-35.
\frac{x+7}{x\left(x-5\right)\left(x+7\right)}+\frac{3x}{x\left(x-5\right)\left(x+7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-5\right) and \left(x-5\right)\left(x+7\right) is x\left(x-5\right)\left(x+7\right). Multiply \frac{1}{x\left(x-5\right)} times \frac{x+7}{x+7}. Multiply \frac{3}{\left(x-5\right)\left(x+7\right)} times \frac{x}{x}.
\frac{x+7+3x}{x\left(x-5\right)\left(x+7\right)}
Since \frac{x+7}{x\left(x-5\right)\left(x+7\right)} and \frac{3x}{x\left(x-5\right)\left(x+7\right)} have the same denominator, add them by adding their numerators.
\frac{4x+7}{x\left(x-5\right)\left(x+7\right)}
Combine like terms in x+7+3x.
\frac{4x+7}{x^{3}+2x^{2}-35x}
Expand x\left(x-5\right)\left(x+7\right).
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}