26. $\frac{4}{4x-1} + \frac{8x-15}{4x^2+11x-3} = \frac{4}{4x-1} + \frac{8x-15}{(4x-1)(x+3)} = \frac{4(x+3) + (8x-15)}{(4x-1)(x+3)} = \frac{4x+12+8x-15}{(4x-1)(x+3)} = \frac{12x-3}{(4x-1)(x+3)} = \frac{3(4x-1)}{(4x-1)(x+3)} = \frac{3}{x+3}$
27. $\frac{9}{2y+3} - \frac{5}{4y} = \frac{9 \cdot 4y - 5(2y+3)}{4y(2y+3)} = \frac{36y - 10y - 15}{4y(2y+3)} = \frac{26y - 15}{4y(2y+3)}$
28. $\frac{4}{5x+7} + \frac{7}{6x} = \frac{4 \cdot 6x + 7(5x+7)}{6x(5x+7)} = \frac{24x + 35x + 49}{6x(5x+7)} = \frac{59x + 49}{6x(5x+7)}$
29. $\frac{1}{3x^2-8x} + \frac{6}{8-3x} = \frac{1}{x(3x-8)} + \frac{6}{-(3x-8)} = \frac{1}{x(3x-8)} - \frac{6}{3x-8} = \frac{1 - 6x}{x(3x-8)}$
30. $\frac{x+4}{3x^2-4x} - \frac{6}{4-3x} = \frac{x+4}{x(3x-4)} - \frac{6}{-(3x-4)} = \frac{x+4}{x(3x-4)} + \frac{6}{3x-4} = \frac{x+4 + 6x}{x(3x-4)} = \frac{7x+4}{x(3x-4)}$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting rational expressions worksheet.
