Mister Exam

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How do you y/(y+3)+y/3+2/y in partial fractions?

You have entered [src]

  y     y   2
----- + - + -
y + 3   3   y

$$\left(\frac{y}{3} + \frac{y}{y + 3}\right) + \frac{2}{y}$$

y/(y + 3) + y/3 + 2/y

General simplification [src]

2   y     y  
- + - + -----
y   3   3 + y

$$\frac{y}{3} + \frac{y}{y + 3} + \frac{2}{y}$$

2/y + y/3 + y/(3 + y)

Fraction decomposition [src]

1 - 3/(3 + y) + 2/y + y/3

$$\frac{y}{3} + 1 - \frac{3}{y + 3} + \frac{2}{y}$$

      3     2   y
1 - ----- + - + -
    3 + y   y   3

Powers [src]

2   y     y  
- + - + -----
y   3   3 + y

$$\frac{y}{3} + \frac{y}{y + 3} + \frac{2}{y}$$

2/y + y/3 + y/(3 + y)

Trigonometric part [src]

2   y     y  
- + - + -----
y   3   3 + y

$$\frac{y}{3} + \frac{y}{y + 3} + \frac{2}{y}$$

2/y + y/3 + y/(3 + y)

Rational denominator [src]

18 + 6*y + y*(3*y + y*(3 + y))
------------------------------
         y*(9 + 3*y)

$$\frac{y \left(y \left(y + 3\right) + 3 y\right) + 6 y + 18}{y \left(3 y + 9\right)}$$

(18 + 6*y + y*(3*y + y*(3 + y)))/(y*(9 + 3*y))

Common denominator [src]

    y    -6 + y 
1 + - - --------
    3    2      
        y  + 3*y

$$\frac{y}{3} - \frac{y - 6}{y^{2} + 3 y} + 1$$

1 + y/3 - (-6 + y)/(y^2 + 3*y)

Assemble expression [src]

2   y     y  
- + - + -----
y   3   3 + y

$$\frac{y}{3} + \frac{y}{y + 3} + \frac{2}{y}$$

2/y + y/3 + y/(3 + y)

Combinatorics [src]

      3            2
18 + y  + 6*y + 6*y 
--------------------
    3*y*(3 + y)

$$\frac{y^{3} + 6 y^{2} + 6 y + 18}{3 y \left(y + 3\right)}$$

(18 + y^3 + 6*y + 6*y^2)/(3*y*(3 + y))

Numerical answer [src]

2.0/y + 0.333333333333333*y + y/(3.0 + y)

2.0/y + 0.333333333333333*y + y/(3.0 + y)

Combining rational expressions [src]

            2        
18 + 6*y + y *(6 + y)
---------------------
     3*y*(3 + y)

$$\frac{y^{2} \left(y + 6\right) + 6 y + 18}{3 y \left(y + 3\right)}$$

(18 + 6*y + y^2*(6 + y))/(3*y*(3 + y))