Title: Ratsionaalavaldiste lihtsustamine/ÜLESANDED (3)

Ilma pealkirjata Question Set

Credits: licence CC BY-SA 4.0

Ratsionaalavaldiste lihtsustamine

Test 3

Lihtsusta avaldis $$\left(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}\right):\left(\dfrac{x^2+y^2}{x^2-y^2}-\dfrac{x+y}{2x-2y}\right)$$ ning leia selle väärtus, kui $$x=2^{-1}$$ ja $$y=1,3^0$$

Q: 1) Avaldise lihtsustamine.

$$\left(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}\right):\left(\dfrac{x^2+y^2}{x^2-y^2}-\dfrac{x+y}{2x-2y}\right)=\dfrac{2A\left(x\:+\:y\right)}{\left(x^2\:+\:B\:+\:y^2\right)}$$

$$A=$$[...], $$B=$$[...]

2) Antud avaldise väärtus, kui $$x=2^{-1}$$ ja $$y=1,3^0$$ on $$\dfrac{L}{N\:}$$, kus $$L=$$[...] ja $$N=$$[...].
A: 1; xy; 12; 7

Lihtsusta avaldis $$\dfrac{a-4}{4a^2-16}+\dfrac{a^3+2a^2+a}{a^4-16}\cdot \left(\dfrac{a-2}{a^2+a}-\dfrac{4-6a}{a^4+2a^3+a^2}\right)$$ ning leia selle väärtus, kui $$a=\sqrt[5]{-32}$$.

Q: 1) Avaldise lihtsustamine.

$$\dfrac{a-4}{4a^2-16}+\dfrac{a^3+2a^2+a}{a^4-16}\cdot \left(\dfrac{a-2}{a^2+a}-\dfrac{4-6a}{a^4+2a^3+a^2}\right)=\dfrac{X}{Y}$$

$$X=$$[...], $$Y=$$[...]

2) Antud avaldise väärtus, kui $$a=\sqrt[5]{-32}$$ on [...].
A: 1; 4a; -0,125
  Hint: Kirjuta vastus kümnendmurruna.

Lihtsusta avaldis $$\dfrac{4m^2-1}{m^3-m^2-m+1}:\left(\dfrac{m}{m^2-2m+1}-\dfrac{1}{1-m}\cdot \dfrac{m}{m+1}-\dfrac{2}{m+1}\right)$$ ning leia selle väärtus, kui $$m=\left(-\dfrac{2}{3}\right)^{-1}$$.

Q: 1) Avaldise lihtsustamine.

a) Tehted sulgudes.

$$\dfrac{m}{m^2-2m+1}-\dfrac{1}{1-m}\cdot \:\dfrac{m}{m+1}-\dfrac{2}{m+1}=\dfrac{Am-B}{\left(m+1\right)\left(m-1\right)^C}$$

$$A=$$[...], $$B=$$[...], $$C=$$[...]

b) Jagamistehe.

$$\dfrac{4m^2-1}{m^3-m^2-m+1}:\left(\dfrac{m}{m^2-2m+1}-\dfrac{1}{1-m}\cdot \dfrac{m}{m+1}-\dfrac{2}{m+1}\right)=\dfrac{Dm+E}{2}$$

$$D=$$[...], $$E=$$[...]

2) Antud avaldise väärtus, kui $$m=\left(-\dfrac{2}{3}\right)^{-1}$$ on [...].
A: 4; 2; 2; 2; 1; -1

Lihtsusta avaldis $$1+\dfrac{x^3+1}{x^3-x^2}:\left(\dfrac{1}{x^2}+\dfrac{1}{x}\cdot \dfrac{x+1}{\left(x-1\right)^2}-\dfrac{1}{1-x+x\left(x-1\right)}\right)$$ ning leia selle väärtus, kui $$x=\left(\dfrac{1}{81}\right)^{-\dfrac{3}{4}}$$.

Lihtsusta avaldis $$1+\dfrac{x^3+1}{x^3-x^2}:\left(\dfrac{1}{x^2}+\dfrac{1}{x}\cdot \dfrac{x+1}{\left(x-1\right)^2}-\dfrac{1}{1-x+x\left(x-1\right)}\right)$$ ning leia selle väärtus, kui $$x=\left(\dfrac{1}{81}\right)^{-\frac{3}{4}}$$.

Q: 1) Avaldise lihtsustamine.

$$1+\dfrac{x^3+1}{x^3-x^2}:\left(\dfrac{1}{x^2}+\dfrac{1}{x}\cdot \dfrac{x+1}{\left(x-1\right)^2}-\dfrac{1}{1-x+x\left(x-1\right)}\right)=A^B$$

$$A=$$[...], $$B=$$[...]

2) Antud avaldise väärtus, kui $$x=\left(\dfrac{1}{81}\right)^{-\dfrac{3}{4}}$$ on [...].
A: x; 2; 729

Lihtsusta avaldis $$\left(\dfrac{p\:}{\:p+3}-\dfrac{4}{p^2+3p}\right):\dfrac{p^2-4}{p^2+8p+15}$$ ning leia selle väärtus, kui $$p=25^{-\frac{1}{2}}$$.

Q: 1) Avaldise lihtsustamine.

$$\left(\dfrac{p\:}{\:p+3}-\dfrac{4}{p^2+3p}\right):\dfrac{p^2-4}{p^2+8p+15}=\dfrac{p+X}{Y}$$

$$X=$$[...], $$Y=$$[...]

2) Antud avaldise väärtus, kui $$p=25^{-\frac{1}{2}}$$ on [...].
A: 5; p; 26