multiply and simplify: 3x+3/x+3 x 2x-1/x^2-1
To multiply and simplify the expression (3x + 3) / (x + 3) * (2x - 1) / (x^2 - 1), we can follow these steps:
Step 1: Factor the numerator and denominator in each fraction if possible.
The first fraction is (3x + 3) / (x + 3).
We can factor out a common factor of 3 in the numerator:
3(x + 1) / (x + 3).
The second fraction is (2x - 1) / (x^2 - 1).
We can factor the denominator using the difference of squares formula:
(x + 1)(x - 1) / (x + 1)(x - 1).
Step 2: Simplify the expression by canceling out common factors.
Now, we have:
[3(x + 1) / (x + 3)] * [(x + 1)(x - 1) / (x + 1)(x - 1)].
We can cancel out the common factors (x + 1) in the numerator and denominator:
[3(x + 1) / (x + 3)] * [(x - 1) / (x - 1)].
Step 3: Multiply the numerators and the denominators.
Let's multiply the numerators and the denominators separately:
[3 * (x + 1) * (x - 1)] / [(x + 3) * (x - 1)].
Step 4: Simplify the expression further, if possible.
We can see that (x - 1) in the numerator and denominator cancels out, leaving us with:
3(x + 1) / (x + 3).
So, the simplified expression is 3(x + 1) / (x + 3).