Multiply and Simplify: Can you please show me the steps on how you get the answer. Thank You
2/4n+6 times n^2+2n-3/n+1
To multiply and simplify the expression (2/4n+6) times (n^2+2n-3/n+1), follow these steps:
Step 1: Factor the expressions if possible.
In the given expression, (n^2+2n-3) and (n+1) cannot be factored further, so leave them as they are.
Step 2: Simplify any common factors between the numerators and denominators.
The numerator (2/4n+6) can be further simplified. Notice that both terms in the numerator (2 and 6) have a common factor of 2. So we can rewrite the expression as (2(1/n+3)).
Step 3: Multiply the numerators together and the denominators together.
Now we have (2(1/n+3)) times (n^2+2n-3/n+1). So we multiply the numerators: (2 * (n^2+2n-3)), and multiply the denominators: ((1/n+3) * (n+1)).
Step 4: Multiply each term individually and combine like terms.
Multiply the numerators:
2 * n^2 = 2n^2
2 * 2n = 4n
2 * -3 = -6
Multiply the denominators:
1 * n = n
1 * 3 = 3
Step 5: Simplify the expression by combining like terms.
Combine the terms in the numerator:
2n^2 + 4n - 6
Combine the terms in the denominator:
n + 3
So, the simplified expression is:
(2n^2 + 4n - 6) / (n + 3)