3/y+2 over 7/y-4 can u please show me the steps on how you got the answer. Thank You
Certainly! To simplify the expression (3/y+2) / (7/y-4), we need to perform the following steps:
Step 1: Simplify the expressions in the numerator and denominator separately.
- In the numerator, we have (3/y + 2).
- To simplify this, we need to find a common denominator for the fraction (3/y).
- The common denominator for (3/y) is y.
- So, we can rewrite (3/y) as (3/y) * (y/y) = 3y/y^2.
- Now, we have (3y/y^2 + 2).
- Since the denominator is the same, we can combine the terms in the numerator to get (3y + 2).
- In the denominator, we have (7/y - 4).
- In this case, there isn't any simplification we can do.
Step 2: Rewrite the expression using the simplified numerator and denominator.
- After simplifying, the expression becomes (3y + 2) / (7/y - 4).
Step 3: Rationalize the denominator.
- The denominator has a fraction (7/y), and we want to eliminate the fraction from the denominator.
- To do this, multiply the numerator and denominator by y (the conjugate of y), which leads to:
- (3y + 2) * y / [(7/y - 4) * y]
- Expanding the denominator, we get (7y - 4y^2).
Step 4: Simplify the expression further if possible.
- If there are any common factors between the numerator and denominator, simplify the expression.
- In this case, there aren't any common factors left to simplify.
Therefore, the simplified form of the expression (3/y+2) / (7/y-4) is (3y + 2) / (7y - 4).