Taller simplificación de fracciones 5
Simplificar las siguientes fracciones
$$1) \frac{4a(a^{2}-x^{2})}{3b\left(c^{2}-x^{2}\right)}\div\left[\frac{a^{2}-ax}{bc+bx}\times\frac{a^{2}+2ax+x^{2}}{c^{2}-2cx+x^{2}}\right]$$
$$2) \frac{x\times(x+a)\times(x+2a)}{3a}-\frac{x\times(x+a)\times(2x+a)}{6a}$$
$$3) \frac{1}{b}\left(\frac{1}{a-b}-\frac{1}{a+2b}\right)-\frac{2}{a^{2}+ab-2b^{2}}$$
$$4) \left(\frac{x+y}{x-y}\right)^{2}-\left(\frac{x-y}{x+y}\right)^{2}$$
$$5) \frac{2}{x-1}+\frac{2}{x+1}-\frac{4x}{x^{2}-x+1}$$
$$6) \left(\frac{x^{2}}{1-x^{4}}+\frac{2x^{4}}{1-x^{8}}\right)\div\left(\frac{x^{2}+1}{x}\right)^{2}$$
$$7) \frac{1}{x}-\frac{1}{(x+1)^{2}}+\frac{2}{x+1}+\frac{x}{1+x+x^{2}}$$
$$8) \frac{1+x^{3}}{1+2x+2×2+x^{3}}$$
$$9) \frac{2x^{3}-9x^{2}+27}{3x^{3}-81x+162}$$
$$10) \frac{a}{b}-\frac{(a^{2}-b^{2})x}{b^{2}}+\frac{a(a^{2}-b^{2})x^{2}}{b^{2}\left(b+ax\right)}$$
$$11) \left\{ \frac{x^{4}-y^{4}}{x^{2}-2ax+a^{2}}\div\frac{x^{2}-ax}{x-a}\right\} \times\frac{x^{5}-a^{2}x^{3}}{x^{3}+a^{3}}\div\left(\frac{x}{a}-\frac{a}{x}\right) $$
$$12) \frac{a^{2}-x^{2}}{a^{2}+ax+x^{2}}\div\frac{\left(1-\frac{a}{x}\right)^{3}\left(1+\frac{a}{x}\right)^{3}}{a^{3}-x^{3}}$$
$$13) \frac{x^{4}-2x^{2}+1}{3x^{5}-10x^{3}+15x-8}$$
$$14) \frac{a^{3}+a(1+a)y+y^{2}}{a^{4}-y^{2}}$$
$$15) \frac{1}{a}+\frac{2}{a+1}+\frac{3}{a+2}-\frac{\frac{4}{a}}{1+\frac{1}{a}}$$
$$16) \frac{x+3}{2x^{2}+9x+9}+\frac{1}{2}\times\frac{1}{2x+}-\left(\frac{a}{a+x}\right)^{2}$$
$$17) \frac{2}{x^{3}+x^{2}+x+1}-\frac{2}{x^{3}-x^{2}+x-1}$$
$$18) \frac{1-a^{2}}{\left(1+ax\right)^{2}-(a+x)^{2}}\div\frac{1}{2}\times\left(\frac{1}{1-x}+\frac{1}{1+x}\right) $$
$$19) \frac{2x^{3}-x^{2}-2x+1}{x^{3}-3x+2}$$
$$20) \frac{x^{2}-6x+8}{4x^{3}-21x^{2}+15x+20}$$
$$21) \frac{2a}{\left(x-2a\right)^{2}}-\frac{x-a}{x^{2}-5ax+6a^{2}}+\frac{2}{x-3a}$$
$$22) \frac{1}{2}\times\left(\frac{a^{2}+x^{2}}{a^{2}-x^{2}}\right)-\frac{1}{2}\times\frac{a+x}{a-x}-\left(\frac{a}{a+x}\right)^{2}$$
$$23) \frac{x}{2}\left(\frac{1}{x-y}-\frac{1}{x+y}\right)\times\frac{x^{2}-y^{2}}{x^{2}y+xy^{2}}\div\frac{1}{x+y}$$
$$24) \frac{1}{x+y}\div\left[\frac{y}{2}\left(\frac{1}{x+y}+\frac{1}{x-y}\right)\times\frac{x^{2}-y^{2}}{x^{2}y+xy^{2}}\right]$$
$$25) \left(3x-5-\frac{2}{x}\right)\times\left(3x+5-\frac{2}{x}\right)\div\left(x-\frac{4}{x}\right) $$
$$26) \left\{ \frac{2}{x}-\frac{1}{a+x}+\frac{1}{a-x}\right\} \div\left\{ \frac{a+x}{a-x}-\frac{a-x}{a+x}\right\} $$
$$27) \frac{1}{2x-1}-\frac{2x-\frac{1}{2x}}{4x^{2}-1}$$
$$28) \left(b+\frac{ab}{b-a}\right)\times\left(b-\frac{ab}{a+b}\right)\times\left(\frac{b^{2}-a^{2}}{b^{2}+a^{2}}\right) $$
$$29) \left\{ x^{3}-\frac{1}{x^{3}}-3\left(x-\frac{1}{x}\right)\right\} \div\left(x-\frac{1}{x}\right) $$
$$30) \frac{2\times\left(x^{2}-\frac{1}{4}\right)}{2x-1}+\frac{1}{2}$$
