Simplify the given rational expressions.
(6m + m ^ 2)/m
(2x - 2)/(x - 1) =
3 (x ^ 2 - 9)/(x + 3) =
(4) (x ^ 2 + 5x + 6)/(x + 3) =
15.x²-16
x2+5x+16
Answer (1)
Answer:Here are the simplified rational expressions: 1. (6m + m^2) / m - Factor out an 'm' from the numerator: m(6 + m) / m- Cancel the common factor 'm': 6 + m Simplified expression: 6 + m2. (2x - 2) / (x - 1) - Factor out a '2' from the numerator: 2(x - 1) / (x - 1)- Cancel the common factor (x - 1): 2 Simplified expression: 23. 3(x^2 - 9) / (x + 3) - Factor the difference of squares in the numerator: 3(x + 3)(x - 3) / (x + 3)- Cancel the common factor (x + 3): 3(x - 3) Simplified expression: 3(x - 3)4. (4)(x^2 + 5x + 6) / (x + 3) - Factor the quadratic in the numerator: 4(x + 2)(x + 3) / (x + 3)- Cancel the common factor (x + 3): 4(x + 2) Simplified expression: 4(x + 2)5. 15x² - 16 / x² + 5x + 16 - This expression cannot be simplified further because there are no common factors between the numerator and denominator. Important Note: When simplifying rational expressions, remember that you cannot cancel terms that are added or subtracted. You can only cancel common factors that are multiplied.
