Algebra 2 Worksheets | Rational Expressions Worksheets - Free Printable

1) $\frac{6z}{8} - \frac{7z - 4}{2z - 9} = \frac{3z(2z - 9) - 4(7z - 4)}{4(2z - 9)} = \frac{6z^2 - 27z - 28z + 16}{4(2z - 9)} = \frac{6z^2 - 55z + 16}{4(2z - 9)}$

2) $\frac{8q}{3q + 2} - \frac{5}{6q - 8} = \frac{8q(6q - 8) - 5(3q + 2)}{(3q + 2)(6q - 8)} = \frac{48q^2 - 64q - 15q - 10}{(3q + 2)(6q - 8)} = \frac{48q^2 - 79q - 10}{(3q + 2)(6q - 8)}$

3) $\frac{7k^4 + 6n^4}{2k^8} - \frac{3k^4 - 8n^4}{2k^8} = \frac{7k^4 + 6n^4 - 3k^4 + 8n^4}{2k^8} = \frac{4k^4 + 14n^4}{2k^8} = \frac{2k^4 + 7n^4}{k^8}$

4) $\frac{2d^2 + 7}{6d^2 + 4} - \frac{3d^2}{6d^2 + 4} = \frac{2d^2 + 7 - 3d^2}{6d^2 + 4} = \frac{-d^2 + 7}{6d^2 + 4} = \frac{7 - d^2}{2(3d^2 + 2)}$

5) $\frac{2}{g^2 + 4g - 12} - \frac{g + 3}{g^2 + 4g - 12} = \frac{2 - (g + 3)}{g^2 + 4g - 12} = \frac{2 - g - 3}{g^2 + 4g - 12} = \frac{-g - 1}{g^2 + 4g - 12} = \frac{-(g + 1)}{(g + 6)(g - 2)}$

6) $\frac{-9}{y^2 - 3y + 2} - \frac{y + 3}{y^2 - 3y + 2} = \frac{-9 - (y + 3)}{y^2 - 3y + 2} = \frac{-9 - y - 3}{y^2 - 3y + 2} = \frac{-y - 12}{y^2 - 3y + 2} = \frac{-(y + 12)}{(y - 1)(y - 2)}$

7) $\frac{7h + 8}{h^2 - 6h - 16} - \frac{6h}{4h} = \frac{7h + 8}{(h - 8)(h + 2)} - \frac{3}{2} = \frac{2(7h + 8) - 3(h - 8)(h + 2)}{2(h - 8)(h + 2)} = \frac{14h + 16 - 3(h^2 - 6h - 16)}{2(h - 8)(h + 2)} = \frac{14h + 16 - 3h^2 + 18h + 48}{2(h - 8)(h + 2)} = \frac{-3h^2 + 32h + 64}{2(h - 8)(h + 2)}$

8) $\frac{5s}{2} - \frac{4s + 5}{3s + 6} = \frac{5s}{2} - \frac{4s + 5}{3(s + 2)} = \frac{5s \cdot 3(s + 2) - 2(4s + 5)}{6(s + 2)} = \frac{15s(s + 2) - 8s - 10}{6(s + 2)} = \frac{15s^2 + 30s - 8s - 10}{6(s + 2)} = \frac{15s^2 + 22s - 10}{6(s + 2)}$

9) $-9 - \frac{x - 3}{x^2 + x - 6} = -9 - \frac{x - 3}{(x + 3)(x - 2)} = \frac{-9(x + 3)(x - 2) - (x - 3)}{(x + 3)(x - 2)} = \frac{-9(x^2 + x - 6) - x + 3}{(x + 3)(x - 2)} = \frac{-9x^2 - 9x + 54 - x + 3}{(x + 3)(x - 2)} = \frac{-9x^2 - 10x + 57}{(x + 3)(x - 2)}$

10) $\frac{8n^7 + 8k^8}{7n^3k^8} - \frac{8n^7 + 5k^8}{7n^3k^8} = \frac{8n^7 + 8k^8 - 8n^7 - 5k^8}{7n^3k^8} = \frac{3k^8}{7n^3k^8} = \frac{3}{7n^3}$