Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
sqrt(x)*(-1+4*x)+(2*x^2-x)/(2*sqrt(x))
How do you sqrt(x)*(-1+4*x)+(2*x^2-x)/(2*sqrt(x)) in partial fractions?
The solution
You have entered
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2
___ 2*x - x
\/ x *(-1 + 4*x) + --------
___
2*\/ x
$$\sqrt{x} \left(4 x - 1\right) + \frac{2 x^{2} - x}{2 \sqrt{x}}$$
sqrt(x)*(-1 + 4*x) + (2*x^2 - x)/((2*sqrt(x)))
Fraction decomposition
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5*x^(3/2) - 3*sqrt(x)/2
$$5 x^{\frac{3}{2}} - \frac{3 \sqrt{x}}{2}$$
___
3/2 3*\/ x
5*x - -------
2
General simplification
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___
\/ x *(-3 + 10*x)
-----------------
2
$$\frac{\sqrt{x} \left(10 x - 3\right)}{2}$$
sqrt(x)*(-3 + 10*x)/2
Rational denominator
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3/2 5/2
- 3*x + 10*x
------------------
2*x
$$\frac{10 x^{\frac{5}{2}} - 3 x^{\frac{3}{2}}}{2 x}$$
(-3*x^(3/2) + 10*x^(5/2))/(2*x)
Numerical answer
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x^0.5*(-1.0 + 4.0*x) + 0.5*x^(-0.5)*(-x + 2.0*x^2)
x^0.5*(-1.0 + 4.0*x) + 0.5*x^(-0.5)*(-x + 2.0*x^2)
Combining rational expressions
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___
\/ x *(-3 + 10*x)
-----------------
2
$$\frac{\sqrt{x} \left(10 x - 3\right)}{2}$$
sqrt(x)*(-3 + 10*x)/2
Powers
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2 x
x - -
___ 2
\/ x *(-1 + 4*x) + ------
___
\/ x
$$\sqrt{x} \left(4 x - 1\right) + \frac{x^{2} - \frac{x}{2}}{\sqrt{x}}$$
sqrt(x)*(-1 + 4*x) + (x^2 - x/2)/sqrt(x)
Common denominator
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___
3/2 3*\/ x
5*x - -------
2
$$5 x^{\frac{3}{2}} - \frac{3 \sqrt{x}}{2}$$
5*x^(3/2) - 3*sqrt(x)/2
Combinatorics
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___
\/ x *(-3 + 10*x)
-----------------
2
$$\frac{\sqrt{x} \left(10 x - 3\right)}{2}$$
sqrt(x)*(-3 + 10*x)/2