Mister Exam
Other calculators
-
How to use it?
- Factor polynomial:
- x^4-9
- a^2+8*a+16
- x^8-y^6
- x^4-81
- Least common denominator:
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- (k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
- k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
- Factor squared:
- -a^4-8*a^2-1
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- x^2-x*a+4*a^2
- How do you in partial fractions?:
- (6x^2+29x)/(x+5)
- (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
- 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
- 1/(n*(n+1)*(n+2))
-
Identical expressions
- (-y*exp(one)/(exp(one)+ one)+(one -y)*exp(one)/((one - one /(exp(one)+ one))*(exp(one)+ one)^ two))/m
- ( minus y multiply by exponent of (1) divide by ( exponent of (1) plus 1) plus (1 minus y) multiply by exponent of (1) divide by ((1 minus 1 divide by ( exponent of (1) plus 1)) multiply by ( exponent of (1) plus 1) squared )) divide by m
- ( minus y multiply by exponent of (one) divide by ( exponent of (one) plus one) plus (one minus y) multiply by exponent of (one) divide by ((one minus one divide by ( exponent of (one) plus one)) multiply by ( exponent of (one) plus one) to the power of two)) divide by m
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)2))/m
- -y*exp1/exp1+1+1-y*exp1/1-1/exp1+1*exp1+12/m
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)²))/m
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1) to the power of 2))/m
- (-yexp(1)/(exp(1)+1)+(1-y)exp(1)/((1-1/(exp(1)+1))(exp(1)+1)^2))/m
- (-yexp(1)/(exp(1)+1)+(1-y)exp(1)/((1-1/(exp(1)+1))(exp(1)+1)2))/m
- -yexp1/exp1+1+1-yexp1/1-1/exp1+1exp1+12/m
- -yexp1/exp1+1+1-yexp1/1-1/exp1+1exp1+1^2/m
- (-y*exp(1) divide by (exp(1)+1)+(1-y)*exp(1) divide by ((1-1 divide by (exp(1)+1))*(exp(1)+1)^2)) divide by m
-
Similar expressions
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1+1/(exp(1)+1))*(exp(1)+1)^2))/m
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)-1))*(exp(1)+1)^2))/m
- (-y*exp(1)/(exp(1)-1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- (y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- (-y*exp(1)/(exp(1)+1)+(1+y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- (-y*exp(1)/(exp(1)+1)-(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)-1)^2))/m
-
Expressions with functions
- Exponent exp
- exp((y+z)^2)/(x+w)-exp(y^2)/x
- exp(2-2*x)/(2*(x-1)^2)+2*(1/(2*(x-1)))*exp(2-2*x)
- exp(x)/x^7-7*exp(x)/x^8
- exp(x)/(2*(e^x+1))-exp(x)/(2*(e^x-1))
- exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2
- Exponent exp
- exp((y+z)^2)/(x+w)-exp(y^2)/x
- exp(2-2*x)/(2*(x-1)^2)+2*(1/(2*(x-1)))*exp(2-2*x)
- exp(x)/x^7-7*exp(x)/x^8
- exp(x)/(2*(e^x+1))-exp(x)/(2*(e^x-1))
- exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2
- Exponent exp
- exp((y+z)^2)/(x+w)-exp(y^2)/x
- exp(2-2*x)/(2*(x-1)^2)+2*(1/(2*(x-1)))*exp(2-2*x)
- exp(x)/x^7-7*exp(x)/x^8
- exp(x)/(2*(e^x+1))-exp(x)/(2*(e^x-1))
- exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2
- Exponent exp
- exp((y+z)^2)/(x+w)-exp(y^2)/x
- exp(2-2*x)/(2*(x-1)^2)+2*(1/(2*(x-1)))*exp(2-2*x)
- exp(x)/x^7-7*exp(x)/x^8
- exp(x)/(2*(e^x+1))-exp(x)/(2*(e^x-1))
- exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2
- Exponent exp
- exp((y+z)^2)/(x+w)-exp(y^2)/x
- exp(2-2*x)/(2*(x-1)^2)+2*(1/(2*(x-1)))*exp(2-2*x)
- exp(x)/x^7-7*exp(x)/x^8
- exp(x)/(2*(e^x+1))-exp(x)/(2*(e^x-1))
- exp(x)/(1-x^2)+2*x*exp(x)/(1-x^2)^2
Expression simplification/
Least common denominator/
(-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
Least common denominator (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
The solution
You have entered
[src]
1 1
-y*e (1 - y)*e
------ + ----------------------
1 2
e + 1 / 1 \ / 1 \
|1 - ------|*\e + 1/
| 1 |
\ e + 1/
-------------------------------
m
$$\frac{\frac{- y e^{1}}{1 + e^{1}} + \frac{\left(1 - y\right) e^{1}}{\left(1 - \frac{1}{1 + e^{1}}\right) \left(1 + e^{1}\right)^{2}}}{m}$$
(((-y)*exp(1))/(exp(1) + 1) + ((1 - y)*exp(1))/(((1 - 1/(exp(1) + 1))*(exp(1) + 1)^2)))/m
General simplification
[src]
1 - y - E*y ----------- m*(1 + E)
$$\frac{- e y - y + 1}{m \left(1 + e\right)}$$
(1 - y - E*y)/(m*(1 + E))
Trigonometric part
[src]
E*y E*(1 - y)
- ----- + --------------------
1 + E 2 / 1 \
(1 + E) *|1 - -----|
\ 1 + E/
------------------------------
m
$$\frac{- \frac{e y}{1 + e} + \frac{e \left(1 - y\right)}{\left(1 + e\right)^{2} \left(1 - \frac{1}{1 + e}\right)}}{m}$$
-(-1 + y + y*cosh(1) + y*sinh(1))
----------------------------------
m*(1 + cosh(1) + sinh(1))
$$- \frac{y + y \sinh{\left(1 \right)} + y \cosh{\left(1 \right)} - 1}{m \left(1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}$$
y*(cosh(1) + sinh(1)) (1 - y)*(cosh(1) + sinh(1))
- --------------------- + ----------------------------------------------------
1 + cosh(1) + sinh(1) / 1 \ 2
|1 - ---------------------|*(1 + cosh(1) + sinh(1))
\ 1 + cosh(1) + sinh(1)/
------------------------------------------------------------------------------
m
$$\frac{- \frac{y \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}{1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}} + \frac{\left(1 - y\right) \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)}{\left(1 - \frac{1}{1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}}\right) \left(1 + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2}}}{m}$$
(-y*(cosh(1) + sinh(1))/(1 + cosh(1) + sinh(1)) + (1 - y)*(cosh(1) + sinh(1))/((1 - 1/(1 + cosh(1) + sinh(1)))*(1 + cosh(1) + sinh(1))^2))/m
Combining rational expressions
[src]
1 - y - E*y ----------- m*(1 + E)
$$\frac{- e y - y + 1}{m \left(1 + e\right)}$$
(1 - y - E*y)/(m*(1 + E))
Powers
[src]
E*y E*(1 - y)
- ----- + --------------------
1 + E 2 / 1 \
(1 + E) *|1 - -----|
\ 1 + E/
------------------------------
m
$$\frac{- \frac{e y}{1 + e} + \frac{e \left(1 - y\right)}{\left(1 + e\right)^{2} \left(1 - \frac{1}{1 + e}\right)}}{m}$$
(-E*y/(1 + E) + E*(1 - y)/((1 + E)^2*(1 - 1/(1 + E))))/m
Assemble expression
[src]
E*y E*(1 - y)
- ------ + ----------------------
1 2
1 + e / 1 \ / 1\
|1 - ------|*\1 + e /
| 1|
\ 1 + e /
---------------------------------
m
$$\frac{- \frac{e y}{1 + e^{1}} + \frac{e \left(1 - y\right)}{\left(1 - \frac{1}{1 + e^{1}}\right) \left(1 + e^{1}\right)^{2}}}{m}$$
(-E*y/(1 + exp(1)) + E*(1 - y)/((1 - 1/(1 + exp(1)))*(1 + exp(1))^2))/m
Combinatorics
[src]
-(-1 + y + E*y) ---------------- m*(1 + E)
$$- \frac{y + e y - 1}{m \left(1 + e\right)}$$
-(-1 + y + E*y)/(m*(1 + E))
Rational denominator
[src]
/ 2 2 2 2\ -1
\E*(1 + E) - E*y*(1 + E) - y*(1 + E) *e /*e
-----------------------------------------------
3
/ 1\
m*\1 + e /
$$\frac{- y \left(1 + e\right)^{2} e^{2} - e y \left(1 + e\right)^{2} + e \left(1 + e\right)^{2}}{e m \left(1 + e^{1}\right)^{3}}$$
(E*(1 + E)^2 - E*y*(1 + E)^2 - y*(1 + E)^2*exp(2))*exp(-1)/(m*(1 + exp(1))^3)
Common denominator
[src]
-(-1 + y + E*y)
----------------
m + E*m
$$- \frac{y + e y - 1}{m + e m}$$
-(-1 + y + E*y)/(m + E*m)