Mister Exam

# Least common denominator x^4/4+5*x^2/2-4*x

An expression to simplify:

### The solution

You have entered [src]
 4      2
x    5*x
-- + ---- - 4*x
4     2        
$$- 4 x + \left(\frac{x^{4}}{4} + \frac{5 x^{2}}{2}\right)$$
x^4/4 + (5*x^2)/2 - 4*x
Fraction decomposition [src]
-4*x + x^4/4 + 5*x^2/2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
        4      2
x    5*x
-4*x + -- + ----
4     2  
General simplification [src]
  /       3       \
x*\-16 + x  + 10*x/
-------------------
4         
$$\frac{x \left(x^{3} + 10 x - 16\right)}{4}$$
x*(-16 + x^3 + 10*x)/4
Factorization [src]
  /           ________________                                                          \ /           ________________                                                          \ /           ________________                          \
|          /         ______  /          ___\                                          | |          /         ______  /          ___\                                          | |          /         ______                           |
|         /      2*\/ 2046   |  1   I*\/ 3 |                      10                  | |         /      2*\/ 2046   |  1   I*\/ 3 |                      10                  | |         /      2*\/ 2046                10          |
x*|x + - 3 /   8 + ---------- *|- - - -------| + ---------------------------------------|*|x + - 3 /   8 + ---------- *|- - + -------| + ---------------------------------------|*|x + - 3 /   8 + ----------  + -----------------------|
|      \/            9       \  2      2   /          ________________                | |      \/            9       \  2      2   /          ________________                | |      \/            9                ________________|
|                                                    /         ______  /          ___\| |                                                    /         ______  /          ___\| |                                    /         ______ |
|                                                   /      2*\/ 2046   |  1   I*\/ 3 || |                                                   /      2*\/ 2046   |  1   I*\/ 3 || |                                   /      2*\/ 2046  |
|                                              3*3 /   8 + ---------- *|- - - -------|| |                                              3*3 /   8 + ---------- *|- - + -------|| |                              3*3 /   8 + ---------- |
\                                                \/            9       \  2      2   // \                                                \/            9       \  2      2   // \                                \/            9      /
$$x \left(x + \left(\frac{10}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}\right)\right) \left(x + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}} + \frac{10}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}}\right)\right) \left(x + \left(- \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}} + \frac{10}{3 \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}}\right)\right)$$
((x*(x - (8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 - i*sqrt(3)/2))))*(x - (8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - (8 + 2*sqrt(2046)/9)^(1/3) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)))
Trigonometric part [src]
        4      2
x    5*x
-4*x + -- + ----
4     2  
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Rational denominator [src]
           4       2
-32*x + 2*x  + 20*x
--------------------
8          
$$\frac{2 x^{4} + 20 x^{2} - 32 x}{8}$$
(-32*x + 2*x^4 + 20*x^2)/8
Common denominator [src]
        4      2
x    5*x
-4*x + -- + ----
4     2  
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Combining rational expressions [src]
  /        /      2\\
x*\-16 + x*\10 + x //
---------------------
4          
$$\frac{x \left(x \left(x^{2} + 10\right) - 16\right)}{4}$$
x*(-16 + x*(10 + x^2))/4
Assemble expression [src]
        4      2
x    5*x
-4*x + -- + ----
4     2  
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Powers [src]
        4      2
x    5*x
-4*x + -- + ----
4     2  
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
0.25*x^4 + 2.5*x^2 - 4.0*x
0.25*x^4 + 2.5*x^2 - 4.0*x
  /       3       \
4         
$$\frac{x \left(x^{3} + 10 x - 16\right)}{4}$$
x*(-16 + x^3 + 10*x)/4