Rational Expressions And Equations (PDF).pdf

1. (4x2y3 + 12x4y – 25x3y5) / (4x2y) = x^2y^2 + 3xy - (25/4)xy^4, domain: y ≠ 0, x ≠ 0
2. (ab – bc + ad – dc) / (ab + bc + ad + dc) = (a - c)(b - d) / (a + c)(b + d), domain: a ≠ -c, b ≠ -d
3. (3a2 + 17ab +10b2) / (6a2 + ab – 2b2) = (3a^2 + 17ab + 10b^2) / (6a^2 + ab - 2b^2), domain: 6a^2 + ab - 2b^2 ≠ 0
4. (x – 4(x+3)) / (x2 – 9) = (x - 4x - 12) / (x^2 - 9) = (-3x - 12) / (x^2 - 9), domain: x ≠ 3, x ≠ -3
5. (3 + 4 + 1) / ((z2 – 13z + 36)(2z2 – 7z – 4)(2z2 – 17z – 9)) = 8 / ((z - 4)(z - 9)(2z + 1)(2z - 4)(2z + 1)(z + 1)), domain: z ≠ 4, z ≠ 9, z ≠ -1/2
6. (2 + 2) / ((x2 – 3x + 2)(x2 – x – 2)) = 4 / ((x - 2)(x - 1)(x + 1)(x - 2)), domain: x ≠ 2, x ≠ 1, x ≠ -1
7. (y-1 – x-1) / (x-1 + y-1) = (1/y - 1/x) / (1/x + 1/y) = (y - x) / (x + y), domain: x ≠ 0, y ≠ 0
8. Solve for x: (2x^2 - 9x - 5) / (x - 5) = (2x + 1) / 2
9. Solve for q: 1/p + 1/q = 1/f
10. Solve for a: (4a + 3) / (a^2 + 11a + 30) - 3 / (a + 6) = 2 / (a + 5)
11. Let's denote the time it takes for Millhouse to dig a trench as M and the time for Bart as B. 1/M + 1/B = 1/2.7, M = B + 1
12. Let's denote the speed of the car as C and the speed of the train as T. C = 2T, 400 / T - 400 / C = 6.5
13. A = k R1 R2 / L^2, 5 = k 30 4 / 10^2, find R1 when A = 4, R2 = 10, L = 5
14. W = k I^2 R, 3 = k 0.1^2 100, find I when W = 4, R = 20