Question

Dividing rational expressions in (21x² -2x-3)/(4x-12)-:(49x² -9) / (x-3) lify your answer as much as possiable

Answer 1

To divide rational expressions, first factor both the numerators and denominators. Then, multiply the expressions and simplify by canceling out common factors. The final answer is (7x + 1) / (28x + 12).

Step-by-step explanation:

To divide rational expressions, we can use the following steps:

1. First, factor both the numerators and denominators.
2. Next, multiply the first rational expression by the reciprocal of the second rational expression.
3. Finally, simplify the resulting expression by canceling out common factors.

Applying these steps to the given expressions:

1. Factor the first numerator: 21x² - 2x - 3 = (7x + 1)(3x - 3).
2. Factor the first denominator: 4x - 12 = 4(x - 3).
3. Factor the second numerator: 49x² - 9 = (7x + 3)(7x - 3).
4. The second denominator is already factored: x - 3.
5. Multiply the expressions: [(7x + 1)(3x - 3)] / [4(x - 3)] * [(x - 3)] / [(7x + 3)(7x - 3)].
6. Cancel out common factors: (7x + 1) / 4 * 1 / (7x + 3) = (7x + 1) / [(4)(7x + 3)].

The final answer is (7x + 1) / (28x + 12).