Question

4а²-1/ а²-9 : 6а²+3/а+3

Answer 1

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Answer 2

To simplify the given expression, we first need to factor the numerator and the denominator of each fraction. Then, we can simplify further by canceling out common factors. Let's start step by step:

Expression: (4a² - 1) / (a² - 9) : (6a² + 3) / (a + 3)

Step 1: Factor the numerator and denominator of each fraction.

Numerator of the first fraction: 4a² - 1 This is a difference of squares, which can be factored as (2a + 1)(2a - 1).

Denominator of the first fraction: a² - 9 This is also a difference of squares, which can be factored as (a + 3)(a - 3).

Numerator of the second fraction: 6a² + 3 Factor out 3 from the numerator: 3(2a² + 1).

Denominator of the second fraction: a + 3

Step 2: Rewrite the expression after factoring:

[(2a + 1)(2a - 1)] / [(a + 3)(a - 3)] : [3(2a² + 1)] / (a + 3)

Step 3: Invert the second fraction and change division to multiplication:

[(2a + 1)(2a - 1)] / [(a + 3)(a - 3)] * [(a + 3) / 3(2a² + 1)]

Step 4: Cancel out common factors:

We can cancel out (a + 3) from the numerator of the first fraction and the denominator of the second fraction.

Result:

(2a - 1) / (a - 3) * 1 / 3(2a² + 1)

Final simplified expression:

(2a - 1) / [3(a - 3)(2a² + 1)]