4 3 2
225 - x + 5*x + 24*x
-----------------------
/ 2 \
x*\-15 + x - 2*x/
$$\frac{- x^{4} + 5 x^{3} + 24 x^{2} + 225}{x \left(x^{2} - 2 x - 15\right)}$$
(225 - x^4 + 5*x^3 + 24*x^2)/(x*(-15 + x^2 - 2*x))
3 - x - 15/x + 75/(8*(3 + x)) + 165/(8*(-5 + x))
$$- x + 3 + \frac{75}{8 \left(x + 3\right)} + \frac{165}{8 \left(x - 5\right)} - \frac{15}{x}$$
15 75 165
3 - x - -- + --------- + ----------
x 8*(3 + x) 8*(-5 + x)
Подстановка условия
[src]
3*x/(x - 1*5) - x + 3*450/((6*x - 1*30)*(x^2 + 3*x)) при x = 1
3*x 1 1
----- - x + 3*--------*450*--------
x - 5 6*x - 30 2
x + 3*x
$$- x + \frac{3 x}{x - 5} + 3 \cdot \frac{1}{6 x - 30} \cdot 450 \cdot \frac{1}{x^{2} + 3 x}$$
4 3 2
225 - x + 5*x + 24*x
-----------------------
/ 2 \
x*\-15 + x - 2*x/
$$\frac{- x^{4} + 5 x^{3} + 24 x^{2} + 225}{x \left(x^{2} - 2 x - 15\right)}$$
$$x = 1$$
4 3 2
225 - (1) + 5*(1) + 24*(1)
-----------------------------
/ 2 \
(1)*\-15 + (1) - 2*(1)/
$$\frac{- (1)^{4} + 5 (1)^{3} + 24 (1)^{2} + 225}{(1) \left((1)^{2} - 2 (1) - 15\right)}$$
4 3 2
225 - 1 + 5*1 + 24*1
-----------------------
/ 2 \
1*\-15 + 1 - 2*1/
$$\frac{- 1^{4} + 5 \cdot 1^{3} + 24 \cdot 1^{2} + 225}{1 \left(-15 - 2 + 1^{2}\right)}$$
$$- \frac{253}{16}$$
3*x 1350
-x + ------ + ----------------------
-5 + x / 2 \
(-30 + 6*x)*\x + 3*x/
$$- x + \frac{3 x}{x - 5} + \frac{1350}{\left(6 x - 30\right) \left(x^{2} + 3 x\right)}$$
-x + 3*x/(-5 + x) + 1350/((-30 + 6*x)*(x^2 + 3*x))
-x + 3.0*x/(-5.0 + x) + 1350.0/((-30.0 + 6.0*x)*(x^2 + 3.0*x))
-x + 3.0*x/(-5.0 + x) + 1350.0/((-30.0 + 6.0*x)*(x^2 + 3.0*x))
/ 4 2 3\
-\-225 + x - 24*x - 5*x /
----------------------------
x*(-5 + x)*(3 + x)
$$- \frac{x^{4} - 5 x^{3} - 24 x^{2} - 225}{x \left(x - 5\right) \left(x + 3\right)}$$
-(-225 + x^4 - 24*x^2 - 5*x^3)/(x*(-5 + x)*(3 + x))
3*x 1350
-x + ----- + ---------------------
x - 5 / 2 \
\x + 3*x/*(6*x - 30)
$$- x + \frac{3 x}{x - 5} + \frac{1350}{\left(6 x - 30\right) \left(x^{2} + 3 x\right)}$$
3*x 1350
-x + ------ + ----------------------
-5 + x / 2 \
(-30 + 6*x)*\x + 3*x/
$$- x + \frac{3 x}{x - 5} + \frac{1350}{\left(6 x - 30\right) \left(x^{2} + 3 x\right)}$$
-x + 3*x/(-5 + x) + 1350/((-30 + 6*x)*(x^2 + 3*x))
Объединение рациональных выражений
[src]
2 2
225 + 3*x *(3 + x) - x *(-5 + x)*(3 + x)
----------------------------------------
x*(-5 + x)*(3 + x)
$$\frac{- x^{2} \left(x - 5\right) \left(x + 3\right) + 3 x^{2} \left(x + 3\right) + 225}{x \left(x - 5\right) \left(x + 3\right)}$$
(225 + 3*x^2*(3 + x) - x^2*(-5 + x)*(3 + x))/(x*(-5 + x)*(3 + x))
Рациональный знаменатель
[src]
1350 3*x
-x + -------------------- + ------
2 3 -5 + x
-90*x - 12*x + 6*x
$$- x + \frac{3 x}{x - 5} + \frac{1350}{6 x^{3} - 12 x^{2} - 90 x}$$
/ 2 \ / 2 \
-6750 + 1350*x + 3*x*(-30 + 6*x)*\x + 3*x/ - x*(-30 + 6*x)*(-5 + x)*\x + 3*x/
-------------------------------------------------------------------------------
/ 2 \
(-30 + 6*x)*(-5 + x)*\x + 3*x/
$$\frac{- x \left(x - 5\right) \left(6 x - 30\right) \left(x^{2} + 3 x\right) + 3 x \left(6 x - 30\right) \left(x^{2} + 3 x\right) + 1350 x - 6750}{\left(x - 5\right) \left(6 x - 30\right) \left(x^{2} + 3 x\right)}$$
(-6750 + 1350*x + 3*x*(-30 + 6*x)*(x^2 + 3*x) - x*(-30 + 6*x)*(-5 + x)*(x^2 + 3*x))/((-30 + 6*x)*(-5 + x)*(x^2 + 3*x))
2
225 + 15*x + 45*x
3 - x + ------------------
3 2
x - 15*x - 2*x
$$- x + \frac{15 x^{2} + 45 x + 225}{x^{3} - 2 x^{2} - 15 x} + 3$$
3 - x + (225 + 15*x^2 + 45*x)/(x^3 - 15*x - 2*x^2)