Mister Exam

Least common denominator ((x*x-11*x+30)/(x*x-9*x+20))/((x*x-36)/(x*x-16))

An expression to simplify:

The solution

You have entered [src]
/x*x - 11*x + 30\
|---------------|
\ x*x - 9*x + 20/
-----------------
/x*x - 36\
|--------|
\x*x - 16/   
$$\frac{\left(\left(- 11 x + x x\right) + 30\right) \frac{1}{\left(- 9 x + x x\right) + 20}}{\left(x x - 36\right) \frac{1}{x x - 16}}$$
((x*x - 11*x + 30)/(x*x - 9*x + 20))/(((x*x - 36)/(x*x - 16)))
Fraction decomposition [src]
1 - 2/(6 + x)
$$1 - \frac{2}{x + 6}$$
      2
1 - -----
6 + x
General simplification [src]
4 + x
-----
6 + x
$$\frac{x + 4}{x + 6}$$
(4 + x)/(6 + x)
Common denominator [src]
      2
1 - -----
6 + x
$$1 - \frac{2}{x + 6}$$
1 - 2/(6 + x)
Rational denominator [src]
/       2\ /      2       \
\-16 + x /*\30 + x  - 11*x/
---------------------------
/       2\ /      2      \
\-36 + x /*\20 + x  - 9*x/
$$\frac{\left(x^{2} - 16\right) \left(x^{2} - 11 x + 30\right)}{\left(x^{2} - 36\right) \left(x^{2} - 9 x + 20\right)}$$
(-16 + x^2)*(30 + x^2 - 11*x)/((-36 + x^2)*(20 + x^2 - 9*x))
Assemble expression [src]
/       2\ /      2       \
\-16 + x /*\30 + x  - 11*x/
---------------------------
/       2\ /      2      \
\-36 + x /*\20 + x  - 9*x/
$$\frac{\left(x^{2} - 16\right) \left(x^{2} - 11 x + 30\right)}{\left(x^{2} - 36\right) \left(x^{2} - 9 x + 20\right)}$$
(-16 + x^2)*(30 + x^2 - 11*x)/((-36 + x^2)*(20 + x^2 - 9*x))
(-16.0 + x^2)*(30.0 + x^2 - 11.0*x)/((-36.0 + x^2)*(20.0 + x^2 - 9.0*x))
(-16.0 + x^2)*(30.0 + x^2 - 11.0*x)/((-36.0 + x^2)*(20.0 + x^2 - 9.0*x))
Powers [src]
/       2\ /      2       \
\-16 + x /*\30 + x  - 11*x/
---------------------------
/       2\ /      2      \
\-36 + x /*\20 + x  - 9*x/
$$\frac{\left(x^{2} - 16\right) \left(x^{2} - 11 x + 30\right)}{\left(x^{2} - 36\right) \left(x^{2} - 9 x + 20\right)}$$
(-16 + x^2)*(30 + x^2 - 11*x)/((-36 + x^2)*(20 + x^2 - 9*x))
Expand expression [src]
(x*x - 16)*(x*x - 11*x + 30)
----------------------------
(x*x - 36)*(x*x - 9*x + 20) 
$$\frac{\left(x x - 16\right) \left(\left(- 11 x + x x\right) + 30\right)}{\left(x x - 36\right) \left(\left(- 9 x + x x\right) + 20\right)}$$
(x*x - 16)*(x*x - 11*x + 30)/((x*x - 36)*(x*x - 9*x + 20))
Combinatorics [src]
4 + x
-----
6 + x
$$\frac{x + 4}{x + 6}$$
(4 + x)/(6 + x)
Combining rational expressions [src]
/       2\
\-16 + x /*(30 + x*(-11 + x))
-----------------------------
/       2\
\-36 + x /*(20 + x*(-9 + x))
$$\frac{\left(x^{2} - 16\right) \left(x \left(x - 11\right) + 30\right)}{\left(x^{2} - 36\right) \left(x \left(x - 9\right) + 20\right)}$$
(-16 + x^2)*(30 + x*(-11 + x))/((-36 + x^2)*(20 + x*(-9 + x)))
Trigonometric part [src]
/       2\ /      2       \
\-16 + x /*\30 + x  - 11*x/
---------------------------
/       2\ /      2      \
\-36 + x /*\20 + x  - 9*x/
$$\frac{\left(x^{2} - 16\right) \left(x^{2} - 11 x + 30\right)}{\left(x^{2} - 36\right) \left(x^{2} - 9 x + 20\right)}$$
(-16 + x^2)*(30 + x^2 - 11*x)/((-36 + x^2)*(20 + x^2 - 9*x))