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\frac{5}{x^{4}}
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\frac{5}{x^{4}}
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\frac{5+3x}{x^{5}\left(\frac{3}{5}+\frac{1}{x}\right)}
Express \frac{\frac{5+3x}{x^{5}}}{\frac{3}{5}+\frac{1}{x}} as a single fraction.
\frac{5+3x}{x^{5}\left(\frac{3x}{5x}+\frac{5}{5x}\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{3}{5} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{5}{5}.
\frac{5+3x}{x^{5}\times \frac{3x+5}{5x}}
Since \frac{3x}{5x} and \frac{5}{5x} have the same denominator, add them by adding their numerators.
\frac{5+3x}{\frac{x^{5}\left(3x+5\right)}{5x}}
Express x^{5}\times \frac{3x+5}{5x} as a single fraction.
\frac{5+3x}{\frac{\left(3x+5\right)x^{4}}{5}}
Cancel out x in both numerator and denominator.
\frac{\left(5+3x\right)\times 5}{\left(3x+5\right)x^{4}}
Divide 5+3x by \frac{\left(3x+5\right)x^{4}}{5} by multiplying 5+3x by the reciprocal of \frac{\left(3x+5\right)x^{4}}{5}.
\frac{5}{x^{4}}
Cancel out 3x+5 in both numerator and denominator.
\frac{5+3x}{x^{5}\left(\frac{3}{5}+\frac{1}{x}\right)}
Express \frac{\frac{5+3x}{x^{5}}}{\frac{3}{5}+\frac{1}{x}} as a single fraction.
\frac{5+3x}{x^{5}\left(\frac{3x}{5x}+\frac{5}{5x}\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{3}{5} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{5}{5}.
\frac{5+3x}{x^{5}\times \frac{3x+5}{5x}}
Since \frac{3x}{5x} and \frac{5}{5x} have the same denominator, add them by adding their numerators.
\frac{5+3x}{\frac{x^{5}\left(3x+5\right)}{5x}}
Express x^{5}\times \frac{3x+5}{5x} as a single fraction.
\frac{5+3x}{\frac{\left(3x+5\right)x^{4}}{5}}
Cancel out x in both numerator and denominator.
\frac{\left(5+3x\right)\times 5}{\left(3x+5\right)x^{4}}
Divide 5+3x by \frac{\left(3x+5\right)x^{4}}{5} by multiplying 5+3x by the reciprocal of \frac{\left(3x+5\right)x^{4}}{5}.
\frac{5}{x^{4}}
Cancel out 3x+5 in both numerator and denominator.
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}