Mister Exam

# How do you ((p-d)/(d^2+p^2))*(((d+p)/d)-(2d/(d-p))) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
 p - d  /d + p    2*d \
-------*|----- - -----|
2    2 \  d     d - p/
d  + p                 
$$\frac{- d + p}{d^{2} + p^{2}} \left(- \frac{2 d}{d - p} + \frac{d + p}{d}\right)$$
((p - d)/(d^2 + p^2))*((d + p)/d - 2*d/(d - p))
Fraction decomposition [src]
1/d
$$\frac{1}{d}$$
1
-
d
General simplification [src]
1
-
d
$$\frac{1}{d}$$
1/d
Rational denominator [src]
        /     2                  \
(p - d)*\- 2*d  + (d + p)*(d - p)/
----------------------------------
/ 2    2\
d*(d - p)*\d  + p /        
$$\frac{\left(- d + p\right) \left(- 2 d^{2} + \left(d - p\right) \left(d + p\right)\right)}{d \left(d - p\right) \left(d^{2} + p^{2}\right)}$$
(p - d)*(-2*d^2 + (d + p)*(d - p))/(d*(d - p)*(d^2 + p^2))
Assemble expression [src]
        /d + p    2*d \
(p - d)*|----- - -----|
\  d     d - p/
-----------------------
2    2
d  + p         
$$\frac{\left(- d + p\right) \left(- \frac{2 d}{d - p} + \frac{d + p}{d}\right)}{d^{2} + p^{2}}$$
(p - d)*((d + p)/d - 2*d/(d - p))/(d^2 + p^2)
Trigonometric part [src]
        /d + p    2*d \
(p - d)*|----- - -----|
\  d     d - p/
-----------------------
2    2
d  + p         
$$\frac{\left(- d + p\right) \left(- \frac{2 d}{d - p} + \frac{d + p}{d}\right)}{d^{2} + p^{2}}$$
(p - d)*((d + p)/d - 2*d/(d - p))/(d^2 + p^2)
Combinatorics [src]
1
-
d
$$\frac{1}{d}$$
1/d
(p - d)*((d + p)/d - 2.0*d/(d - p))/(d^2 + p^2)
(p - d)*((d + p)/d - 2.0*d/(d - p))/(d^2 + p^2)
Powers [src]
        /d + p    2*d \
(p - d)*|----- - -----|
\  d     d - p/
-----------------------
2    2
d  + p         
$$\frac{\left(- d + p\right) \left(- \frac{2 d}{d - p} + \frac{d + p}{d}\right)}{d^{2} + p^{2}}$$
(p - d)*((d + p)/d - 2*d/(d - p))/(d^2 + p^2)
Common denominator [src]
1
-
d
$$\frac{1}{d}$$
1/d
Combining rational expressions [src]
        /     2                  \
(p - d)*\- 2*d  + (d + p)*(d - p)/
----------------------------------
/ 2    2\
d*(d - p)*\d  + p /        
$$\frac{\left(- d + p\right) \left(- 2 d^{2} + \left(d - p\right) \left(d + p\right)\right)}{d \left(d - p\right) \left(d^{2} + p^{2}\right)}$$
(p - d)*(-2*d^2 + (d + p)*(d - p))/(d*(d - p)*(d^2 + p^2))