Taller simplificación de fracciones 4
Simplificar las siguientes fracciones.
$$1) \frac{1}{x+y}-\frac{1}{x-y}+\frac{2x}{x^{2}-y^{2}}$$
$$2) \frac{1}{2x+y}+\frac{1}{2x-y}-\frac{3x}{4x^{2}-y^{2}}$$
$$3) \frac{5}{1+2x}-\frac{3x}{1-2x}-\frac{4-13x}{1-4x^{2}}$$
$$4) \frac{2a}{2a+3b}+\frac{3b}{2a-3b}-\frac{8b^{2}}{4a^{2}-9b^{2}}$$
$$5) \frac{1}{a+x}+\frac{1}{(a+x)^{2}}-\frac{1}{a^{2}-x^{2}}$$
$$6) \frac{10}{9-a^{2}}-\frac{2}{3+a}-\frac{1}{3-a}$$
$$7) \frac{5x}{6\left(x^{2}-1\right)}-\frac{1}{2(x-1)}+\frac{1}{3(x+1)}$$
$$8) \frac{1}{2(a-b)}-\frac{1}{2(a+b)}-\frac{b}{a^{2}-b^{2}}$$
$$9) \frac{1}{1+x}+\frac{2}{1-x^{2}}+\frac{3}{(1+x)^{2}}$$
$$10) \frac{2a}{2a-3}-\frac{5}{6a+9}-\frac{4(3a+2)}{3(4a^{2}-9)}$$
$$11) \frac{3}{x-2}+\frac{2}{3x+6}+\frac{5x}{x^{2}-4}$$
$$12) \frac{x}{x^{3}+y^{3}}-\frac{y}{x^{3}-y^{3}}+\frac{x^{3}y+xy^{3}}{x^{6}-y^{6}}$$
$$13) \frac{1}{x^{2}-9x+20}+\frac{1}{x^{2}-11x+30}$$
$$14) \frac{1}{x^{2}-7x+12}-\frac{1}{x^{2}-5x+6}$$
$$15) \frac{1}{2x^{2}-x-1}-\frac{1}{2x^{2}+x-3}$$
$$16) \frac{1}{2x^{2}-x-1}-\frac{3}{6x^{2}-x-2}$$
$$17) \frac{4}{4-7a-2a^{2}}-\frac{3}{3-a-10a^{2}}$$
$$18) \frac{5}{5+x-18x^{2}}-\frac{2}{2+5x+2x^{2}}$$
$$19) \frac{1}{x+1}-\frac{1}{\left(x+1\right)(x+2)}+\frac{1}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$
$$20) \frac{5x}{2(x+1)(x-3)}-\frac{15(x-1)}{16(x-3)(x-2)}-\frac{9(x+3)}{16(x+1)(x-2)}$$
