Mister Exam

Other calculators

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

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))
Numerical answer [src] 
(-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))
    © Mister Exam – Calculator