Talleres de Álgebra

Talleres de Álgebra

Suma y Resta de varias Fracciones

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) $\frac{5x}{2(x+1)(x-3)}-\frac{15(x-1)}{16(x-3)(x-2)}-\frac{9(x+3)}{16(x+1)(x-2)}$