Evaluate
\frac{2\left(x^{12}+3\right)}{x^{6}}
Expand
\frac{2\left(x^{12}+3\right)}{x^{6}}
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2x\left(x^{5}+\frac{3}{x^{7}}\right)
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
2x\left(\frac{x^{5}x^{7}}{x^{7}}+\frac{3}{x^{7}}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{5} times \frac{x^{7}}{x^{7}}.
2x\times \frac{x^{5}x^{7}+3}{x^{7}}
Since \frac{x^{5}x^{7}}{x^{7}} and \frac{3}{x^{7}} have the same denominator, add them by adding their numerators.
2x\times \frac{x^{12}+3}{x^{7}}
Do the multiplications in x^{5}x^{7}+3.
\frac{2\left(x^{12}+3\right)}{x^{7}}x
Express 2\times \frac{x^{12}+3}{x^{7}} as a single fraction.
\frac{2x^{12}+6}{x^{7}}x
Use the distributive property to multiply 2 by x^{12}+3.
\frac{\left(2x^{12}+6\right)x}{x^{7}}
Express \frac{2x^{12}+6}{x^{7}}x as a single fraction.
\frac{2x^{12}+6}{x^{6}}
Cancel out x in both numerator and denominator.
2x\left(x^{5}+\frac{3}{x^{7}}\right)
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
2x\left(\frac{x^{5}x^{7}}{x^{7}}+\frac{3}{x^{7}}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{5} times \frac{x^{7}}{x^{7}}.
2x\times \frac{x^{5}x^{7}+3}{x^{7}}
Since \frac{x^{5}x^{7}}{x^{7}} and \frac{3}{x^{7}} have the same denominator, add them by adding their numerators.
2x\times \frac{x^{12}+3}{x^{7}}
Do the multiplications in x^{5}x^{7}+3.
\frac{2\left(x^{12}+3\right)}{x^{7}}x
Express 2\times \frac{x^{12}+3}{x^{7}} as a single fraction.
\frac{2x^{12}+6}{x^{7}}x
Use the distributive property to multiply 2 by x^{12}+3.
\frac{\left(2x^{12}+6\right)x}{x^{7}}
Express \frac{2x^{12}+6}{x^{7}}x as a single fraction.
\frac{2x^{12}+6}{x^{6}}
Cancel out x 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}