Ratsionaal­avaldiste lihtsustamine 1

\left(\frac{2-a}{1+2a}-\frac{2-b}{1+2b}\right)\ :\ \left[1+\frac{\left(2-a\right)\left(2-b\right)}{\left(1+2a\right)\left(1+2b\right)}\right] = 

\left(\frac{x-5}{x-3}-\frac{y-1}{y-2}\right)\ :\ \left(5-\frac{x+7y-17}{y-2}\right) = 

\left(\frac{a+1}{2a-2}-\frac{6}{2-2a^2}-\frac{a+3}{2a+2}\right)\cdot\frac{4a^3-4a}{5} = 

\left(\frac{2x}{x+2}+\frac{2x}{6-3x}+\frac{8x}{x^2-4}\right)\ :\ \frac{4x^2+16x}{x-2} = 

\left(\frac{5}{2a+3}+\frac{2}{3-2a}+\frac{2a+9}{4a^2-9}\right)\ :\ \frac{8}{4a^2+12a+9} = 

\left(\frac{1}{2a-b}+\frac{3b}{b^2-4a^2}-\frac{2}{2a+b}\right)\ :\ \left(\frac{4a^2+b^2}{4a^2-b^2}+1\right) = 

\frac{4a^2-1}{\left(a^2-1\right)\left(a-1\right)}\ :\ \left(\frac{a}{a^2-2a+1}+\frac{2-a}{a^2-1}\right)-\frac{1}{2} = 

\left[\frac{a^2+1}{\left(a^2-1\right)\left(a-1\right)}-\frac{a}{a^2-2a+1}\right]\cdot\frac{a^2-1}{a+2}-\frac{2}{a^2+2a} = 

\left(\frac{1}{a}+\frac{a^2}{b^3}\right)\ :\ \left(\frac{1}{a}-\frac{1}{b}+\frac{a}{b^2}\right)\ :\ \frac{\left(a-b\right)^2+4ab}{1+\frac{b}{a}} = 

\left[2-\frac{x}{y}\ :\ \left(2+\frac{x}{y}\right)+\frac{x}{y}\ :\ \left(2-\frac{x}{y}\right)\right]\cdot\frac{\frac{y}{2}+\frac{x^3}{2y^2}}{\left(x+y\right)^2-3xy} = 

\left(\frac{a-3}{a^2-3a+9}-\frac{6a-18}{a^3+27}\right)\ :\ \frac{5a-15}{4a^3+108} = 

Siis on avaldise väärtus  = .

\frac{6x-30}{3x^3-24}\ :\ \left(\frac{10x-29}{x^3-8}-\frac{x+2}{x^2+2x+4}\right)= 

Siis on avaldise väärtus  = .

\left(\frac{1}{2-4a}+\frac{a+1}{8a^3-1}\cdot\frac{4a^2+2a+1}{1+2a}\right)\ :\ \frac{1}{4a-2} = 

\left(\frac{1}{2-6a}+\frac{1}{27a^3-1}\ :\ \frac{1+3a}{1+3a+9a^2}\right)\cdot\frac{2+6a}{a} = 

\left(\frac{4x}{x+2}-\frac{x^3-8}{x^3+8}\cdot\frac{4x^2-8x+16}{x^2-4}\right)\ :\ \frac{16}{x+2} = 

Siis on avaldise väärtus  = .

\left(\frac{8a}{a-1}-\frac{8a\left(3a^2+3a+3\right)}{a^3+27}\ :\ \frac{a^3-1}{a^2-3a+9}\right)\cdot\frac{a+3}{8a^2}= 

Siis on avaldise väärtus  = .

\frac{a^2}{a^2-2a+1}-\frac{a^2+a}{a^3-1}\cdot\left(\frac{a}{a^2-1}+\frac{1}{a^2-a}\right) = 

\frac{m^2}{m^2+2m+1}-\frac{m^2-m}{1+m^3}\cdot\left(\frac{m}{m^2-1}-\frac{1}{m^2+m}\right) = 

\left(\frac{x}{y^2+xy}+\frac{x-y}{x^2-xy}\right)\ :\ \left(\frac{y^2}{x^3-xy^2}+\frac{1}{x-y}\right) = 

\left(\frac{a^2}{a^2-a^3b}-\frac{1}{1+ab}\right)\ :\ \left(\frac{2+a^2b^2}{1-a^3b^3}-\frac{1}{1+ab+a^2b^2}\right) = 

\left[\left(\frac{a-1}{a^3-a}-\frac{a}{a^3+2a^2+a}+\frac{1}{a+1}\right)\ :\ \frac{a^4-a}{a^3-a}-\frac{1}{a}\right]\cdot\frac{1-a^2}{a} = 

\left(\frac{1}{x^2-bx}-\frac{3b^2}{x^4-xb^3}-\frac{b}{x^3+bx^2+b^2x}\right)\cdot\left(b+\frac{x^3-x^2}{2x+2b}\ :\ \frac{x-1}{2}\right) =