Ecuaciones fraccionarias

1. $\frac{2}{3}(x+1)-\frac{1}{7}(x+5)=1$.

2. $\frac{6}{7}(x-9)-\frac{1}{3}(5-x)+3x+1=0$.

3. $\frac{1}{3}(5x-24)+\frac{1}{7}(x-2)-2(x-1)=0$.

4. ${\displaystyle \frac{x+3}{4}}+{\displaystyle \frac{7x-2}{5}}={\displaystyle \frac{5x-1}{4}}+{\displaystyle \frac{5x+4}{9}}$.

5. ${\displaystyle \frac{x+1}{3}}-{\displaystyle \frac{x-1}{4}}={\displaystyle \frac{x-2}{5}}-{\displaystyle \frac{x-3}{6}}+{\displaystyle \frac{31}{60}}$.

6. ${\displaystyle \frac{(2x-1)(2-x)}{2}}+x^2-{\displaystyle \frac{1+3x}{2}}=0$.

7. ${\displaystyle \frac{6x-11}{4}}-{\displaystyle \frac{3-4x}{6}}={\displaystyle \frac{4}{3}}-{\displaystyle \frac{x}{8}}$.

8. ${\displaystyle \frac{x+6}{4}}-{\displaystyle \frac{16-3x}{12}}=4\frac{1}{6}$.

9. $x-{\displaystyle \frac{x-2}{3}}={\displaystyle \frac{x+23}{4}}-{\displaystyle \frac{10+x}{5}}$.

10. ${\displaystyle \frac{5x+3}{x-1}}+{\displaystyle \frac{2x-3}{2x-1}}=6$.

11. ${\displaystyle \frac{3x}{4x+1}}+1=2-{\displaystyle \frac{x}{2(2x-1)}}$.

12. ${\displaystyle \frac{8x+7}{5x+4}}-1=1-{\displaystyle \frac{2x}{5x+1}}$.

13. ${\displaystyle \frac{x+1}{2(x-1)}}-{\displaystyle \frac{x-1}{x+1}}={\displaystyle \frac{17-x^2}{2(x^2-1)}}$.

Si los denominadores contienen expresiones tanto simples como compuestas, por lo general es mejor eliminar primero las expresiones simples y después las compuestas. Después de cada multiplicación, el resultado debe reducirse a su forma más simple.

1. Resuelve ${\displaystyle \frac{4x+3}{10}}-{\displaystyle \frac{2x+3}{5x-1}}={\displaystyle \frac{2x-1}{5}}$.

lint Multiplicar por $10$, 4x + 3 - 10(2x + 3)5x - 1 = 4x - 2. lint Transponer, 4x + 3 - 4x + 2 = 10(2x + 3)5x - 1. lint Combinar, 5 = 10(2x + 3)5x - 1. [1] lint Dividir por $5$, 1 = 2(2x + 3)5x - 1. lint Multiplicar por $5x-1$, 5x - 1 = 4x + 6. lint Transponer y combinar, x = 7.

Ejercicio 53.

Resuelve:

1. ${\displaystyle \frac{10x+13}{18}}-{\displaystyle \frac{x+2}{x-3}}={\displaystyle \frac{5x-4}{9}}$.

2. ${\displaystyle \frac{6x+7}{10}}-{\displaystyle \frac{3x+1}{5}}={\displaystyle \frac{x-1}{3x-4}}$.

3. ${\displaystyle \frac{11x-12}{14}}-{\displaystyle \frac{11x-7}{19x+7}}={\displaystyle \frac{22x-36}{28}}$.