Mister Exam
How do you sqrt(2x+1)*1/(2x+1)*2 in partial fractions?
The solution
You have entered
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_________ \/ 2*x + 1 -----------*2 2*x + 1
$$2 \frac{\sqrt{2 x + 1}}{2 x + 1}$$
(sqrt(2*x + 1)/(2*x + 1))*2
Fraction decomposition
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2/sqrt(1 + 2*x)
$$\frac{2}{\sqrt{2 x + 1}}$$
2 ----------- _________ \/ 1 + 2*x
General simplification
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2 ----------- _________ \/ 1 + 2*x
$$\frac{2}{\sqrt{2 x + 1}}$$
2/sqrt(1 + 2*x)
Numerical answer
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2.82842712474619*(0.5 + x)^0.5/(1.0 + 2.0*x)
2.82842712474619*(0.5 + x)^0.5/(1.0 + 2.0*x)
Rational denominator
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_________ 2*\/ 1 + 2*x ------------- 1 + 2*x
$$\frac{2 \sqrt{2 x + 1}}{2 x + 1}$$
2*sqrt(1 + 2*x)/(1 + 2*x)
Common denominator
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2 ----------- _________ \/ 1 + 2*x
$$\frac{2}{\sqrt{2 x + 1}}$$
2/sqrt(1 + 2*x)
Trigonometric part
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2 ----------- _________ \/ 1 + 2*x
$$\frac{2}{\sqrt{2 x + 1}}$$
2/sqrt(1 + 2*x)
Assemble expression
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2 ----------- _________ \/ 1 + 2*x
$$\frac{2}{\sqrt{2 x + 1}}$$
2/sqrt(1 + 2*x)
Combining rational expressions
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2 ----------- _________ \/ 1 + 2*x
$$\frac{2}{\sqrt{2 x + 1}}$$
2/sqrt(1 + 2*x)