Mister Exam

# How do you ((2*x+10)/(3*x))/(2*x^2+20*x+50*x) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
    /2*x + 10\
|--------|
\  3*x   /
------------------
2
2*x  + 20*x + 50*x
$$\frac{\frac{1}{3 x} \left(2 x + 10\right)}{50 x + \left(2 x^{2} + 20 x\right)}$$
((2*x + 10)/((3*x)))/(2*x^2 + 20*x + 50*x)
Fraction decomposition [src]
-2/(245*(35 + x)) + 1/(21*x^2) + 2/(245*x)
$$- \frac{2}{245 \left(x + 35\right)} + \frac{2}{245 x} + \frac{1}{21 x^{2}}$$
       2           1       2
- ------------ + ----- + -----
245*(35 + x)       2   245*x
21*x         
General simplification [src]
    5 + x
-------------
2
3*x *(35 + x)
$$\frac{x + 5}{3 x^{2} \left(x + 35\right)}$$
(5 + x)/(3*x^2*(35 + x))
Expand expression [src]
        2*x + 10
------------------------
/   2              \
3*x*\2*x  + 20*x + 50*x/
$$\frac{2 x + 10}{3 x \left(50 x + \left(2 x^{2} + 20 x\right)\right)}$$
(2*x + 10)/(3*x*(2*x^2 + 20*x + 50*x))
Rational denominator [src]
     10 + 2*x
-----------------
/   2       \
3*x*\2*x  + 70*x/
$$\frac{2 x + 10}{3 x \left(2 x^{2} + 70 x\right)}$$
(10 + 2*x)/(3*x*(2*x^2 + 70*x))
Assemble expression [src]
     10 + 2*x
-----------------
/   2       \
3*x*\2*x  + 70*x/
$$\frac{2 x + 10}{3 x \left(2 x^{2} + 70 x\right)}$$
(10 + 2*x)/(3*x*(2*x^2 + 70*x))
0.333333333333333*(10.0 + 2.0*x)/(x*(2.0*x^2 + 70.0*x))
0.333333333333333*(10.0 + 2.0*x)/(x*(2.0*x^2 + 70.0*x))
Combinatorics [src]
    5 + x
-------------
2
3*x *(35 + x)
$$\frac{x + 5}{3 x^{2} \left(x + 35\right)}$$
(5 + x)/(3*x^2*(35 + x))
Common denominator [src]
    5 + x
-------------
3        2
3*x  + 105*x 
$$\frac{x + 5}{3 x^{3} + 105 x^{2}}$$
(5 + x)/(3*x^3 + 105*x^2)
Powers [src]
     10 + 2*x
-----------------
/   2       \
3*x*\2*x  + 70*x/
$$\frac{2 x + 10}{3 x \left(2 x^{2} + 70 x\right)}$$
    10   2*x
-- + ---
3     3
---------------
/   2       \
x*\2*x  + 70*x/
$$\frac{\frac{2 x}{3} + \frac{10}{3}}{x \left(2 x^{2} + 70 x\right)}$$
(10/3 + 2*x/3)/(x*(2*x^2 + 70*x))
Trigonometric part [src]
     10 + 2*x
-----------------
/   2       \
3*x*\2*x  + 70*x/
$$\frac{2 x + 10}{3 x \left(2 x^{2} + 70 x\right)}$$
(10 + 2*x)/(3*x*(2*x^2 + 70*x))
Combining rational expressions [src]
    5 + x
-------------
2
3*x *(35 + x)
$$\frac{x + 5}{3 x^{2} \left(x + 35\right)}$$
(5 + x)/(3*x^2*(35 + x))