Title: Ratsionaalavaldiste lihtsustamine/ÜLESANDED (2)

Ilma pealkirjata Question Set

Credits: licence CC BY-SA 4.0

Ratsionaalavaldiste lihtsustamine

Test 2

Uuri avaldise $$\left(\dfrac{m^2-mx}{m^2x+x^3}-\dfrac{2m^2}{x^3-mx^2+m^2x-m^3}\right)\cdot \left(1-\dfrac{x-1}{m}-\dfrac{x}{m^2}\right)$$ lihtsustamise käiku ning leia puuduvad suurused.

Q: 1) $$\dfrac{m^2-mx}{m^2x+x^3}-\dfrac{2m^2}{x^3-mx^2+m^2x-m^3}=\dfrac{m^2-mx}{x\left(m^2+x^2\right)}^{^{(A}}-\dfrac{2m^{2\:}}{A\left(x^2+m^2\right)}^{^{(x}}=\dfrac{-m^3-mx^2}{Ax\left(m^2+x^2\right)}=$$

$$=\dfrac{-m\left(m^2+x^2\right)}{Ax\left(m^2+x^2\right)}=\dfrac{m}{mx-x^2}$$

$$A=$$[...]

2) $$1^{(m^2}-\dfrac{x-1^{(B}}{m}-\dfrac{x^(1}{m^2}=\dfrac{m^2-mx+m-x}{m^2}=\dfrac{C\left(m+1\right)}{m^2}$$

$$B=$$[...]

$$C=$$[...]

3)$$\dfrac{m}{mx-x^2}\cdot \dfrac{\left(m+1\right)\left(m-x\right)}{m^2}=\dfrac{m\cdot \left(m+1\right)\left(m-x\right)}{T\left(m-x\right)\cdot m^2}=\dfrac{K}{mx}$$

$$T=$$[...]

$$K=$$[...]
A: x-m; m; m-x; x; m+1

Uuri avaldise $$\left(\dfrac{3a}{\:1-3a}+\dfrac{2a}{3a+1}\right):\dfrac{6a^2+10a}{1-6a+9a^2}$$ lihtsustamiskäiku ning leia puuduvad suurused.

Q: $$\left(\dfrac{3a}{\:1-3a}+\dfrac{2a}{3a+1}\right):\dfrac{6a^2+10a}{1-6a+9a^2}=\dfrac{Xa^2+Ya}{\left(3a+1\right)\left(-3a+1\right)}:\dfrac{2a\left(3a+Y\right)}{\left(3a-1\right)^2}=$$

$$=\dfrac{a\left(Xa+Y\right)\cdot \left(3a-1\right)^2}{\left(3a+1\right)\left(-3a+1\right)\cdot 2a\left(3a+Y\right)}=-\dfrac{3a-1}{Za+2}$$

$$X=$$[...]

$$Y=$$[...]

$$Z=$$[...]
A: 3; 5; 6

Lihtsusta avaldis.

Q: $$\dfrac{5a^2-a}{6a^2-3ax+2a-x}\cdot \dfrac{3a+1}{5a-1}-\dfrac{2a^2}{4a^2-x^2}=\dfrac{Tx}{Ra^2-x^2}$$

$$T=$$[...]

$$R=$$[...]
A: a; 4

Lihtsusta avaldis $$\left(p-q+\dfrac{4q^2-p^2}{p+q}\right):\left(\dfrac{p}{p^2-q^2}+\dfrac{2}{q-p}+\dfrac{1}{p+q}\right)$$.

Q: Lihtsusta avaldis $$\left(p-q+\dfrac{4q^2-p^2}{p+q}\right):\left(\dfrac{p}{p^2-q^2}+\dfrac{2}{q-p}+\dfrac{1}{p+q}\right)$$.
- $$q^2-pq$$ (correct)
- $$\dfrac{3q}{p^2-q}$$
- $$\dfrac{3q^2}{p+q}$$
- $$-\dfrac{3q}{\left(p-q\right)\left(p+q\right)}$$
- $$3p^2-pq$$

Uuri avaldise $$\dfrac{m}{\:am-2a^2}-\dfrac{2}{m^2+m-2am-2a}\cdot \left(1+\dfrac{3m+m^2}{3+m}\right)$$ lahenduskäiku ning leia puuduvad suurused.

Uuri avaldise $$\dfrac{m}{\:am-2a^2}-\dfrac{2}{m^2+m-2am-2a}\cdot \left(1+\dfrac{3m+m^2}{3+m}\right)$$ lihtsustamise lahenduskäiku ning leia puuduvad suurused.

Q: 1) $$1^{(3+m}+\dfrac{3m+m^2}{3+m}=\dfrac{3+m+X+m^2}{3+m}=\dfrac{m^2+Y+3}{3+m}=\dfrac{Z\left(m+3\right)}{3+m}=m+1$$

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

2) $$\dfrac{2}{m^2+m-2am-2a}\cdot \left(m+1\right)=\dfrac{2\cdot \left(m+1\right)}{\left(m+1\right)\left(m-W\right)}=\dfrac{2}{m-W}$$

3) $$\dfrac{m}{\:am-2a^2}-\dfrac{m}{m-W}=\dfrac{m^{(1}}{a\left(m-2a\right)}-\dfrac{2^{(a}}{m-W}=\dfrac{m-2a}{a\left(m-2a\right)}=\dfrac{P}{a}$$

$$W=$$[...]

$$P=$$[...]
A: 3m; 4m; m+1; 2a; 1

Uuri avaldise $$\left(\dfrac{25}{a^2+5a+25}-\dfrac{2a}{a-5}-\dfrac{a^3+25a^2}{a^3-125}\right)\cdot \left(a-5+\dfrac{15a}{a-5}\right)$$ lihtsustamiskäiku ning leia puuduvad suurused.

Q: $$\left(\dfrac{25}{a^2+5a+25}-\dfrac{2a}{a-5}-\dfrac{a^3+25a^2}{a^3-125}\right)\cdot \left(a-5+\dfrac{15a}{a-5}\right)=$$

$$=\dfrac{25\left(a-5\right)+2a\left(a^2+5a+\color{blue} {x}\right)-a^3-25a^2}{\left(a-5\right)\left(a^2+5a+25\right)}\cdot \dfrac{a^2-\color{blue} {y}+25+15a}{a-5}=$$

$$=\dfrac{25a-125+2a^3+10a^2+\color{blue} {z}-a^3-25a^2}{\left(a-5\right)\left(a^2+5a+25\right)}\cdot \:\dfrac{a^2+5a+25}{a-5}=\dfrac{a^3-15a^2+\color{blue} {w}-125}{\left(a-5\right)\left(a^2+5a+25\right)}\cdot \:\dfrac{a^2+5a+25}{a-5}=$$

$$=\dfrac{\left(a-5\right)^{\color{blue} {q}}\left(a^2+5a+25\right)}{\left(a-5\right)\left(a^2+5a+25\right)\left(a-5\right)}=\color{blue} {t}$$

$$\color{blue} {x}=$$[...], $$\color{blue} {y}=$$[...], $$\color{blue} {z}=$$[...], $$\color{blue} {w}=$$[...], $$\color{blue} {q}=$$[...], $$\color{blue} {t}=$$[...]
A: 25; 10a; 50a; 75a; 3; a-5