Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^3+64
- x1*x2+x1^2*x3^2+x2*x3
- 49-m^2
- 2*x^3+3*x^2+3*x+1
- Least common denominator:
- ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
- (y/x-y+x/x+y)/(1/x2/y2)
- ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
- (x/sqrt(x^2-8))-(7*x/(x^2-8+7*(sqrt(x^2-8))))
- Factor squared:
- -y^4-14*y^2-2
- x^2-9*x-5
- 2*p^2+3*p-2
- x^2-x-2
- How do you in partial fractions?:
- (t^4+9)/(t^4+9t^2)
- sin^(-1)(sin((9pi)/(8)))
- 2/(x+2)-(2*x-6)/(x+2)^2
- (5*a^2+3*a-2)/(a^2-1)
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Identical expressions
- ((x*x^(one / two)-x)^ three)/(((x^(three / four)- one)/(x^(one / four)- one)-x^(one / two))*(one -x))^ three
- ((x multiply by x to the power of (1 divide by 2) minus x) cubed ) divide by (((x to the power of (3 divide by 4) minus 1) divide by (x to the power of (1 divide by 4) minus 1) minus x to the power of (1 divide by 2)) multiply by (1 minus x)) cubed
- ((x multiply by x to the power of (one divide by two) minus x) to the power of three) divide by (((x to the power of (three divide by four) minus one) divide by (x to the power of (one divide by four) minus one) minus x to the power of (one divide by two)) multiply by (one minus x)) to the power of three
- ((x*x(1/2)-x)3)/(((x(3/4)-1)/(x(1/4)-1)-x(1/2))*(1-x))3
- x*x1/2-x3/x3/4-1/x1/4-1-x1/2*1-x3
- ((x*x^(1/2)-x)³)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))³
- ((x*x to the power of (1/2)-x) to the power of 3)/(((x to the power of (3/4)-1)/(x to the power of (1/4)-1)-x to the power of (1/2))*(1-x)) to the power of 3
- ((xx^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))(1-x))^3
- ((xx(1/2)-x)3)/(((x(3/4)-1)/(x(1/4)-1)-x(1/2))(1-x))3
- xx1/2-x3/x3/4-1/x1/4-1-x1/21-x3
- xx^1/2-x^3/x^3/4-1/x^1/4-1-x^1/21-x^3
- ((x*x^(1 divide by 2)-x)^3) divide by (((x^(3 divide by 4)-1) divide by (x^(1 divide by 4)-1)-x^(1 divide by 2))*(1-x))^3
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Similar expressions
- ((x*x^(1/2)-x)^3)/(((x^(3/4)+1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
- ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1+x))^3
- ((x*x^(1/2)+x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
- ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)+1)-x^(1/2))*(1-x))^3
- ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)+x^(1/2))*(1-x))^3
Expression simplification/
Least common denominator/
((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
Least common denominator ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
The solution
You have entered
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3
/ ___ \
\x*\/ x - x/
------------------------------
3
// 3/4 \ \
|| x - 1 ___| |
||--------- - \/ x |*(1 - x)|
||4 ___ | |
\\\/ x - 1 / /
$$\frac{\left(\sqrt{x} x - x\right)^{3}}{\left(\left(1 - x\right) \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)\right)^{3}}$$
(x*sqrt(x) - x)^3/(((x^(3/4) - 1)/(x^(1/4) - 1) - sqrt(x))*(1 - x))^3
General simplification
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3 3
/ 4 ___\ / 3/2 \
\-1 + \/ x / *\x - x/
-------------------------
3
/ ___\ 3
\1 - \/ x / *(-1 + x)
$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - \sqrt{x}\right)^{3} \left(x - 1\right)^{3}}$$
(-1 + x^(1/4))^3*(x^(3/2) - x)^3/((1 - sqrt(x))^3*(-1 + x)^3)
Trigonometric part
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3
/ 3/2 \
\x - x/
--------------------------------
3
/ 3/4 \
3 | ___ -1 + x |
(1 - x) *|- \/ x + ----------|
| 4 ___|
\ -1 + \/ x /
$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$
(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)
Combining rational expressions
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3 3
/ 4 ___\ / 3/2 \
\-1 + \/ x / *\x - x/
------------------------------------------
3
3 / 3/4 ___ / 4 ___\\
(1 - x) *\-1 + x - \/ x *\-1 + \/ x //
$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(x^{\frac{3}{4}} - \sqrt{x} \left(\sqrt[4]{x} - 1\right) - 1\right)^{3}}$$
(-1 + x^(1/4))^3*(x^(3/2) - x)^3/((1 - x)^3*(-1 + x^(3/4) - sqrt(x)*(-1 + x^(1/4)))^3)
Numerical answer
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(x^1.5 - x)^3/((1.0 - x)^3*(-x^0.5 + (-1.0 + x^0.75)/(-1.0 + x^0.25))^3)
(x^1.5 - x)^3/((1.0 - x)^3*(-x^0.5 + (-1.0 + x^0.75)/(-1.0 + x^0.25))^3)
Rational denominator
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3 3 3
/ ___\ / 4 ___\ / 3/2 \
-\1 + \/ x / *\-1 + \/ x / *\x - x/
----------------------------------------
6
(-1 + x)
$$- \frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(\sqrt{x} + 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(x - 1\right)^{6}}$$
-(1 + sqrt(x))^3*(-1 + x^(1/4))^3*(x^(3/2) - x)^3/(-1 + x)^6
Assemble expression
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3
/ 3/2 \
\x - x/
--------------------------------
3
/ 3/4 \
3 | ___ -1 + x |
(1 - x) *|- \/ x + ----------|
| 4 ___|
\ -1 + \/ x /
$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$
(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)
Combinatorics
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3 3
/ 4 ___\ / 3/2\
\-1 + \/ x / *\x - x /
-------------------------
3
3 / ___\
(-1 + x) *\-1 + \/ x /
$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(- x^{\frac{3}{2}} + x\right)^{3}}{\left(\sqrt{x} - 1\right)^{3} \left(x - 1\right)^{3}}$$
(-1 + x^(1/4))^3*(x - x^(3/2))^3/((-1 + x)^3*(-1 + sqrt(x))^3)
Common denominator
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2 5/2 ___ 15/4 7/2 9/2 21/4 11/2 13/4 17/4 3 3/2
14 14 - 84*x - 60*x - 42*\/ x - 24*x - 18*x - 10*x - 3*x + 3*x + 3*x + 9*x + 18*x + 91*x + 103*x
- -- - x - --------------------------------------------------------------------------------------------------------------------------------
3 3 3/2 9/2 ___ 4 2 5/2
-3 - 24*x - 24*x - 3*x + 9*\/ x + 9*x + 18*x + 18*x
$$- x - \frac{14}{3} - \frac{- 3 x^{\frac{21}{4}} + 18 x^{\frac{17}{4}} - 24 x^{\frac{15}{4}} + 9 x^{\frac{13}{4}} + 3 x^{\frac{11}{2}} - 10 x^{\frac{9}{2}} - 18 x^{\frac{7}{2}} - 60 x^{\frac{5}{2}} + 103 x^{\frac{3}{2}} - 42 \sqrt{x} + 91 x^{3} - 84 x^{2} + 3 x + 14}{- 3 x^{\frac{9}{2}} + 18 x^{\frac{5}{2}} - 24 x^{\frac{3}{2}} + 9 \sqrt{x} + 9 x^{4} - 24 x^{3} + 18 x^{2} - 3}$$
-14/3 - x - (14 - 84*x^2 - 60*x^(5/2) - 42*sqrt(x) - 24*x^(15/4) - 18*x^(7/2) - 10*x^(9/2) - 3*x^(21/4) + 3*x + 3*x^(11/2) + 9*x^(13/4) + 18*x^(17/4) + 91*x^3 + 103*x^(3/2))/(-3 - 24*x^3 - 24*x^(3/2) - 3*x^(9/2) + 9*sqrt(x) + 9*x^4 + 18*x^2 + 18*x^(5/2))
Powers
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3
/ 3/2 \
\x - x/
--------------------------------
3
/ 3/4 \
3 | ___ -1 + x |
(1 - x) *|- \/ x + ----------|
| 4 ___|
\ -1 + \/ x /
$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$
(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)