X.

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

If the denominators contain both simple and compound expressions, it is generally best to remove the simple expressions first, and then the compound expressions. After each multiplication the result should be reduced to the simplest form.

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

lint Multiply by $10$, 4x + 3 - 10(2x + 3)5x - 1 = 4x - 2. lint Transpose, 4x + 3 - 4x + 2 = 10(2x + 3)5x - 1. lint Combine, 5 = 10(2x + 3)5x - 1. [1] lint Divide by $5$, 1 = 2(2x + 3)5x - 1. lint Multiply by $5x-1$, 5x - 1 = 4x + 6. lint Transpose and combine, x = 7.

Exercise 53.

Solve: