Fraction decomposition
[src]
-1/(8 + x)^2 - x/8 + 1/(8*(8 + x))
$$- \frac{x}{8} + \frac{1}{8 \left(x + 8\right)} - \frac{1}{\left(x + 8\right)^{2}}$$
1 x 1
- -------- - - + ---------
2 8 8*(8 + x)
(8 + x)
General simplification
[src]
/ 2 \
-x*\63 + x + 16*x/
--------------------
2
512 + 8*x + 128*x
$$- \frac{x \left(x^{2} + 16 x + 63\right)}{8 x^{2} + 128 x + 512}$$
-x*(63 + x^2 + 16*x)/(512 + 8*x^2 + 128*x)
x*(0.125*(-8.0 + x)/(8.0 + x) - 0.125*(8.0 + x)*(-8.0 + x))/(-64.0 + x^2)
x*(0.125*(-8.0 + x)/(8.0 + x) - 0.125*(8.0 + x)*(-8.0 + x))/(-64.0 + x^2)
x x
- - + ------------------
8 2
512 + 8*x + 128*x
$$- \frac{x}{8} + \frac{x}{8 x^{2} + 128 x + 512}$$
-x/8 + x/(512 + 8*x^2 + 128*x)
Assemble expression
[src]
/ (-8 + x)*(8 + x) -8 + x \
x*|- ---------------- + ---------|
\ 8 8*(8 + x)/
----------------------------------
2
-64 + x
$$\frac{x \left(- \frac{\left(x - 8\right) \left(x + 8\right)}{8} + \frac{x - 8}{8 \left(x + 8\right)}\right)}{x^{2} - 64}$$
x*(-(-8 + x)*(8 + x)/8 + (-8 + x)/(8*(8 + x)))/(-64 + x^2)
/ x \
|-1 + - |
| 8 (-8 + x)*(8 + x)|
x*|------ - ----------------|
\8 + x 8 /
-----------------------------
2
-64 + x
$$\frac{x \left(\frac{\frac{x}{8} - 1}{x + 8} - \frac{\left(x - 8\right) \left(x + 8\right)}{8}\right)}{x^{2} - 64}$$
/ (-8 + x)*(8 + x) -8 + x \
x*|- ---------------- + ---------|
\ 8 8*(8 + x)/
----------------------------------
2
-64 + x
$$\frac{x \left(- \frac{\left(x - 8\right) \left(x + 8\right)}{8} + \frac{x - 8}{8 \left(x + 8\right)}\right)}{x^{2} - 64}$$
x*(-(-8 + x)*(8 + x)/8 + (-8 + x)/(8*(8 + x)))/(-64 + x^2)
-x*(7 + x)*(9 + x)
-------------------
2
8*(8 + x)
$$- \frac{x \left(x + 7\right) \left(x + 9\right)}{8 \left(x + 8\right)^{2}}$$
-x*(7 + x)*(9 + x)/(8*(8 + x)^2)
Combining rational expressions
[src]
/ 2\
x*\1 - (8 + x) /*(-8 + x)
-------------------------
/ 2\
8*\-64 + x /*(8 + x)
$$\frac{x \left(1 - \left(x + 8\right)^{2}\right) \left(x - 8\right)}{8 \left(x + 8\right) \left(x^{2} - 64\right)}$$
x*(1 - (8 + x)^2)*(-8 + x)/(8*(-64 + x^2)*(8 + x))
/ (-8 + x)*(8 + x) -8 + x \
x*|- ---------------- + ---------|
\ 8 8*(8 + x)/
----------------------------------
2
-64 + x
$$\frac{x \left(- \frac{\left(x - 8\right) \left(x + 8\right)}{8} + \frac{x - 8}{8 \left(x + 8\right)}\right)}{x^{2} - 64}$$
x*(-(-8 + x)*(8 + x)/8 + (-8 + x)/(8*(8 + x)))/(-64 + x^2)
Rational denominator
[src]
/ 2 \
x*\-8 + x - (8 + x) *(-8 + x)/
------------------------------
/ 2\
\-64 + x /*(64 + 8*x)
$$\frac{x \left(x - \left(x - 8\right) \left(x + 8\right)^{2} - 8\right)}{\left(8 x + 64\right) \left(x^{2} - 64\right)}$$
x*(-8 + x - (8 + x)^2*(-8 + x))/((-64 + x^2)*(64 + 8*x))