Simplify the following algebraic expressions: 1. (4x+2)/2 2. (9a2-3)/(-3) 3. (8y2+4y-1)/4 4. (6a-4b+2c)/(-2) 5. (5x2-10x)/x, x!=0

Hey Ona💘💘💋💞, good to see you again. Here are the solutions to the problems: 1. Simplify (4x+2)/(2) Step 1: Divide each term in the numerator by the denominator. (4x+2)/(2) = (4x)/(2) + (2)/(2) Step 2: Simplify each term. = 2x + 1 The simplified expression is 2x+1. 2. Simplify (9a^2-3)/(-3) Step 1: Divide each term in the numerator by the denominator. (9a^2-3)/(-3) = (9a^2)/(-3) - (3)/(-3) Step 2: Simplify each term. = -3a^2 - (-1) = -3a^2 + 1 The simplified expression is -3a^2+1. 3. Simplify (8y^2+4y-1)/(4) Step 1: Divide each term in the numerator by the denominator. (8y^2+4y-1)/(4) = (8y^2)/(4) + (4y)/(4) - (1)/(4) Step 2: Simplify each term. = 2y^2 + y - (1)/(4) The simplified expression is 2y^2+y-(1)/(4). 4. Simplify (6a-4b+2c)/(-2) Step 1: Divide each term in the numerator by the denominator. (6a-4b+2c)/(-2) = (6a)/(-2) - (4b)/(-2) + (2c)/(-2) Step 2: Simplify each term. = -3a - (-2b) + (-c) = -3a + 2b - c The simplified expression is -3a+2b-c. 5. Simplify (5x^2-10x)/(x), x ≠ 0 Step 1: Divide each term in the numerator by the denominator. (5x^2-10x)/(x) = (5x^2)/(x) - (10x)/(x) Step 2: Simplify each term. = 5x - 10 The simplified expression is 5x-10. 6. Simplify (4a^4+a^2)/(-a^2), a ≠ 0 Step 1: Divide each term in the numerator by the denominator. (4a^4+a^2)/(-a^2) = (4a^4)/(-a^2) + (a^2)/(-a^2) Step 2: Simplify each term. = -4a^4-2 + (-1) = -4a^2 - 1 The simplified expression is -4a^2-1. 7. Simplify (3x^3-6x^2-3x)/(-3x), x ≠ 0 Step 1: Divide each term in the numerator by the denominator. (3x^3-6x^2-3x)/(-3x) = (3x^3)/(-3x) - (6x^2)/(-3x) - (3x)/(-3x) Step 2: Simplify each term. = -x^3-1 - (-2x^2-1) - (-1) = -x^2 + 2x + 1 The simplified expression is -x^2+2x+1. 8. Simplify (-5m^4-10m^2-15m^2)/(5m), m ≠ 0 Step 1: Combine like terms in the numerator. (-5m^4-10m^2-15m^2)/(5m) = (-5m^4-25m^2)/(5m) Step 2: Divide each term in the numerator by the denominator. = (-5m^4)/(5m) - (25m^2)/(5m) Step 3: Simplify each term. = -m^4-1 - 5m^2-1 = -m^3 - 5m The simplified expression is -m^3-5m. 9. Simplify (7y^3-4y^2)/(y^2), y ≠ 0 Step 1: Divide each term in the numerator by the denominator. (7y^3-4y^2)/(y^2) = (7y^3)/(y^2) - (4y^2)/(y^2) Step 2: Simplify each term. = 7y^3-2 - 4y^2-2 = 7y - 4y^0 = 7y - 4 The simplified expression is 7y-4. 10. Simplify (-16a^4+8a^3-4a^2)/(-4a^2), a ≠ 0 Step 1: Divide each term in the numerator by the denominator. (-16a^4+8a^3-4a^2)/(-4a^2) = (-16a^4)/(-4a^2) + (8a^3)/(-4a^2) - (4a^2)/(-4a^2) Step 2: Simplify each term. = 4a^4-2 - 2a^3-2 - (-1) = 4a^2 - 2a + 1 The simplified expression is 4a^2-2a+1. 11. Simplify (15b^3-5b^2+10)/(5b^2), b ≠ 0 Step 1: Divide each term in the numerator by the denominator. (15b^3-5b^2+10)/(5b^2) = (15b^3)/(5b^2) - (5b^2)/(5b^2) + (10)/(5b^2) Step 2: Simplify each term. = 3b^3-2 - 1 + (2)/(b^2) = 3b - 1 + (2)/(b^2) The simplified expression is 3b-1+(2)/(b^2). 12. Simplify (24x^3y-18x^2y^2+30xy^3)/(6xy), x, y ≠ 0 Step 1: Divide each term in the numerator by the denominator. (24x^3y-18x^2y^2+30xy^3)/(6xy) = (24x^3y)/(6xy) - (18x^2y^2)/(6xy) + (30xy^3)/(6xy) Step 2: Simplify each term. = 4x^3-1y^1-1 - 3x^2-1y^2-1 + 5x^1-1y^3-1 = 4x^2y^0 - 3xy + 5x^0y^2 = 4x^2 - 3xy + 5y^2 The simplified expression is 4x^2-3xy+5y^2. 13. Simplify (-14m^4n^2+21m^3n^2-7m^2n)/(-7m^2n), m, n ≠ 0 Step 1: Divide each term in the numerator by the denominator. (-14m^4n^2+21m^3n^2-7m^2n)/(-7m^2n) = (-14m^4n^2)/(-7m^2n) + (21m^3n^2)/(-7m^2n) - (7m^2n)/(-7m^2n) Step 2: Simplify each term. = 2m^4-2n^2-1 - 3m^3-2n^2-1 - (-1) = 2m^2n - 3mn + 1 The simplified expression is 2m^2n-3mn+1. 14. Simplify (18a^4b^4-27a^3b^3+3)/(3a^2b^2), a, b ≠ 0 Step 1: Divide each term in the numerator by the denominator. (18a^4b^4-27a^3b^3+3)/(3a^2b^2) = (18a^4b^4)/(3a^2b^2) - (27a^3b^3)/(3a^2b^2) + (3)/(3a^2b^2) Step 2: Simplify each term. = 6a^4-2b^4-2 - 9a^3-2b^3-2 + (1)/(a^2b^2) = 6a^2b^2 - 9ab + (1)/(a^2b^2) The simplified expression is 6a^2b^2-9ab+(1)/(a^2b^2). Drop the next question! 📸